180rpm to 360 rpm, unlike 12000rpm on optical discs, was how fast floppy disks got.
I am not sure, whether all drives had the same speed, but 360rpm is not close to the physical stress limitations of floppy disks.
Why were floppy disks not any faster? Because of a technical limitation?
Their speed of 18×512×(rpm/60) bytes per second was easily sufficient for plain/hypertext documents without multimedia attached to it.
As you mentioned, speed was considered sufficient for the typical applications at the time they were introduced. Also, any significant rotational speed increase would have meant:
More complex data separator circuitry (due to higher bandwidth needed), probably better shielding on the r/w head wiring and drive-to-controller cabling -> cost, development effort
Higher risk of drive/media damage if there is some imperfection in the media, or if any foreign matter gets into the drive or between media and sleeve (observable with hard drives. Dust in a hard drive can wreck it.) -> reliability
More wear from media-to-sleeve friction - 5 1/4" and 8" discs typically touched the sleeve, which was lined with soft material -> wear, noise
The disc didn't always get perfectly centered by the loading mechanism, leading to rotational imbalance -> vibration, noise, wear
Probably also time needed to accelerate the medium to that speed without causing stress -> perceived speed, and/or cost due to much more complex electronics to read before medium is up to speed. If media is clamped with the motor on (as done in many existing floppy systems), mind the stress to the material if that is done at high speed!
Designing media so that it kept structurally sound even if punctured, driven against the read/write head by vibration/shock, suddenly braked in case something jams (observable with CD-ROM - high speed drives can rip damaged media to pieces!)
Also mind that very early (8 inch era) drives did not use controllable BLDC motors but synchronous AC motors that might have posed some limitations (and made these limitations into specs).
That answer is somewhat trivial:
Hard disks and optical drives are contact-less technologies - Nothing touches (or is even allowed to touch) the media while it spins. On a hard disk or CD-ROM, the heads touching the media would end up with catastrophic effects.
Floppies and tape drives are different. The heads are constantly touching the media directly while it moves. You obviously want this to happen at a much lower relative speed to avoid wear on both the heads and media - Even if floppy disks were specifically teflon-coated to remove friction.
"Really floppy" disks of the 8" and 5-1/4" type also have constant friction between inner sleeve and media while rotating. That has somewhat improved with hard-case technologies of the 3" and 3-1/2" type.
In a sense, floppies are like hard disks, but designed to survive a constant head crash.
I used to work for a company called ‘Rimage’ who manufactured robotic duplicators for floppy disks, the company still exists and today manufactures robotic equipment to publish/duplicate cd, dvd and Blu-ray.
The fastest rotational speed for a floppy disk was 1440 rpm and the equipment would also write to both sides of the disk at the same time. This meant you could duplicate a 1.4MB disk in less than 20 seconds.
The drives used could be modified versions of consumer drives such as Sony 73W which ran at 600 rpm, but YE Data produced a drive especially for this industry and it ran at 1440 rpm for duplicating.
There were, in fact, attempts to create faster floppy drives.
Corporate Systems Center once sold a high-speed floppy drive called the X10 Accelerated Floppy Drive. The drive came with a special controller card with its own processor and memory, and it basically read both sides of the disk concurrently and at four times the normal spindle speed, allowing it to load the whole disk in about five seconds. The memory was used as a write-back cache to speed up writes to the disk.
Some floppy-based Sony Mavica digital cameras used a high-speed floppy drive that were capable of reading and writing to disks at two or four times the normal speed using a higher spindle speed. This was particularly useful because it greatly shortened shot-to-shot times; the camera had to write each image to the disk before it could shoot another.
As noted by several other answers, floppy disks weren't really designed to handle these high speeds. I have a Mavica FD-90 with the 4x floppy drive and it was distinctly less reliable than any of the PC floppy drives I've used. I've had disks jam inside the drive, and in one case, a partial disassembly of the camera was required to eject the disk. I would suppose that because of a lack of market interest and cost concerns, nobody made floppy disks specifically for high-speed drives.
I have a video of the FD-90 in action here.
Many computers had floppy drives that couldn't process data as fast as it came from a disk, even at 300rpm. If the time required to process a sector is twice as long as the time required to read it, reading all the sectors on a track would require that the disk rotate about three times. If the drive were to spin twice as fast, the time required to process each sector would be four times the (now shorter) time to read it, making it necessary for the disk to rotate five times. Doubling the rotational speed of the drive would thus only reduce the required time by 16% rather than by 50%.
To make matters worse, getting good performance out of a floppy generally requires that the disk be in a position to read out a sector just before the computer is ready to receive the data. If the drive is spinning fast enough that the disk rotates past a sector just before the computer is ready for the data, it will generally be necessary to wait an extra revolution. While reading 16 sectors on a normal-speed drive with 3:1 interleave would take about three revolutions at 200ms each (600ms total) reading those same 16 sectors on a "double speed" drive would require 19 revolutions, or about 1.9 seconds. Unless the data was written with a 5:1 interleave (which would add 66% to the time required to read it on a normal-speed drive), the faster drive would read it much more slowly than a slower one.
The limitations of floppy drives were not mechanical. While they certainly couldn't have stood up to the 15000 RPM that some hard drives today have, they were certainly more than capable of being read much faster than the old hardware would have you believe.
There were a number of things that hindered older hardware, including a slower interface to the motherboard (fewer maximum bits per second), poor programming practices (floppy drivers not aligning DMA buffers to 64KB boundaries), and so on.
Later disk drives were able to perform much better by having an IDE interface. For example, the LS120 was capable of writing the entire contents of a 1.44MB image to a 3.5" floppy in just a couple of seconds, probably at least 15 times faster than older systems. Anecdotally, this was a problem for me; I'd often format a floppy more than once, since it happened so quickly I wasn't sure it'd happened at all.
Even the older drives using the older interface could achieve much higher speeds if programmed with optimal DMA transfers and a sufficiently beefy processor. Floppies were slow back then, but they didn't have to be. I actually found a MS-DOS driver a few decades ago that aligned the DMA buffers to a 64kb boundary, and I was able to write 1.44MB of data to the disk in about 10 seconds, while the MS-DOS driver took almost 33 seconds to transfer the same amount of data.
If you have an older system, you might try doing some research on DMA programming and floppy drive interfaces to figure out if you can write something that runs much faster on older hardware. You'll just need a basic understanding of DMA, ports, memory, and some machine code. The firmware will stop your drive from destroying it and/or the disk, but if you spend some time researching this, you could actually get some serious speed.
The main limitation was the speed with which the computer could process the data from the drive. To keep costs low standard floppy drives were fairly simple devices, relying on the computer to do the decoding and detect things like the start of track markers.
Later faster floppy drives became available. 2x USB floppy drives were not uncommon, and even 4x units existed. However those had their own custom controllers to handle the higher rotation speed and thus data rate.
For example, consider the classic Intel 8272A and NEC UPD765A floppy controllers, which were very common PCs from the 80s.
Both parts operate from an 8MHz clock, relatively fast in the 1980s when CPUs were typically running at 1 to 5MHz. As speeds get above about 10MHz special consideration is needed to make the electronics work reliably, which increases cost and complexity.
Note that at 8MHz both those parts are limited to single and double density disks. They can't even handle 1.5MB high density disks at this speed. And this is dedicated controller hardware, earlier systems that used the CPU to control the drive directly in order to reduce costs were limited to single density (350kB) 3.5" disks or 5.25" disks.
The 400kb and later double-sided 800kb and bigger Classic Macintosh floppies did run faster, depending on head location.
One of the Mac innovations was variable-speed drives see http://lowendmac.com/2016/floppy-disk-compatibility-and-incompatibility-in-the-mac-world/
These drives had a variable speed motor that allowed the Mac to pack 400K into a disk that would only hold 360 KB on a fixed-speed drive. (This is also the reason non-Mac computers can’t mount 400K and 800K Mac floppy disks.)
My first Mac was a 1985 512KB "Fat Mac" with the internal 400kb drive, for which I purchased a third party 800kb double-sided. They definitely varied in speed - you could hear it.
I wonder if varying in speed also allows the drive to maintain a more uniform density of writing over the increased circumference of the tracks.
I just dug out my paper copy of Inside Macintosh Vol IV which on page 251 says With double-sided disks a single mechanism positions two read/write heads - one above the disk and one below - so that the drive can access two tracks simultaneously...This lets the drive read or write two complete tracks of information before it has to move the heads....The double-sided drive controls its own motor speed, ignoring the speed signal (PWM) from the Analog Signal Generator (ASG).
It is a limitation of the media -- which operates at lower audio frequencies. Magnetic media has a similar limitation across the board in all technology. In other words, it is a purely analog medium.
