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.