First of all it's a matter of timing - with no double sided drives available, there is no choice between either. 5.25 drives were first introduced by Shugart with the SA-400 single sided 35 track drive. There was no double sided drive available at all. It wasn't until Tandon introduced the double sided TM-100-2.
Second, it's a matter of profit - low manufacturing cost plus high sales price equals good profit (*1).
Third, it needs the will to upgrade instead of just continuing good sales (*2).
Bottom line: Parts alone play only a minor role, if at all.
It would be tempting to explain this by saying, well of course the double-sided drives cost more
Which they do.
so would be found in a serious business computer that is not as price-sensitive as machines like the Atari 8-bits and the Commodore 64.
Don't forget it's as well a matter of need. Small systems, especially home computers rarely have the need access large amount of data. Most of the time it's at maximum a memory full of data - as in loading a game.
Business systems in contrast are way less about code than all about data - also a reason why banked memory extensions like the Saturn for the Apple II, or later LIM on the PC, where such a big deal in business installations. They are of only limited use for code, but as good as main memory when it comes to data.
But then again, the Apple II floppy drive did not need to be particularly price-sensitive, and was very definitely for business use; the company was explicitly being told by business customers that a disk drive and an 80 column display were the two features at the top of the wish list.
That's more of an assumption in hindsight using later marketing material. The Disk II drive was constructed with an extreme angle on price. This is not at least documented by the way Jobs interacted with Shugart. Shortly after they introduced the first 5.25 Drive, the SA-400, Jobs went there to get some. But instead of paying OEM price of 390 USD Shugart called, he wanted to have a drive for less than 100 USD. Long story short, Apple ended up with buying the SA-400 without electronics (now called SA-390) and adding one designed by Wozniak. Of course, at that price it had only a single head.
With a sales price of 600 USD, the Disk II became a fountain of profit.
Intuitively, it feels like a single and double-sided floppy drive should not be very different in cost;
It isn't huge but substantial
it's just one extra component,
I guess you mean the second head, which needs also a second assembly and of course large parts of the analogue circuitry doubled.
the saving of which might be offset by needing an extra SKU.
Only if one offers both types of drives. The same way as IBM only offered double sided drives, saving that SKU, Apple only had single sided, doing the same.
Sometimes small cost differences translate to large price differences because market segmentation. But if that's what's going on here, the Apple case is surprising.
Since when is profit optmization a surprise - not everyone thinks like an engineer - that's especially the case for Mr. Jobs.
Likewise Apple never extended that to 40 tracks - which wouldn't have cost any additional hardware - or more. Not even with later machines and complete different drives(*3)
The Apple Disk II was introduced three years before the IBM PC. Was there some technical reason why the cost of double-sided drives, declined sharply during those years?
Not so much as there was the introduction of MFM drives. It's important to keep in mind that Apple's, as well as Commodore's (which offered dual sided early on) GCR systems were only of advantage (*4) in the small time gap between FM and MFM being available at similar cost. When MFM controllers came down in price around 1979/1980, they could store more data onto the same drives than FM and GCR.
Just what was the difference in manufacturing cost between the two kinds of drives during those years, anyway?
Well for one the single/double sided issue goes back until IBM times and 8 Inch drives, but more so prices changed a lot and very quickly (*5). I guess the original drive that brought us the 5.25 disk would make the most relevant cornerstone:
In 1977 the SA-400 single sided was introduced at 390 USD for OEM and 425 USD street price. The same drive was soon after specified for 40 tracks without changing designation or price.
The 1978 SA-450 was for most parts the same drive but double sided (and 40 tracks from the start) and introduced at 450 USD.
Putting those two number (425 vs 450) together might look like a 5% difference, but it isn't a good match (*6), as it's a year apart, a year with Tandon offering better drives at lower price.
*1 - Perfect to be wasted on vanity projects.
*2 - It's not really part of US management philosophy to let engineers improve without pressure.
*3 - Like Commodore did in 1980 by introducing dual sided 80 track with the 8050 drives.
*4 - Original 35 track SA-400 could store 80 KiB with FM encoding, while Woz' GCR implementation could do originally 114 KiB and later 140 KiB. MFM in turn would do ~148 KiB on the same drive - not to mention that by then 40 tracks was standard thus giving up to 180 KiB.
*5 - Well Shugart was not only 'fortunate' to sell in big numbers, but as well hunted by Tandon who first extended the drive to 40 tracks and first introduced a double sided one.
*6 - The only comparable price list I have is of 1982, way too late for this.