Considering how mechanisms would have to work, a coil is probably required, anyway. The technological end date is more thematic than a hardline of technological progress, anyway. Toady's opposed to steampunk dwarves riding trains and firing guns, but water clocks, dungeons that involve spikes repeatedly springing from the ground based upon gears tied to a minecart, and something like the Antikythera Mechanism is fine, since it "feels Medieval fantasy".
Like I said springs themselves are pretty appropriate and traps are planned to be made more complex. I was just pointing the date out because personally I find the idea of coiled mattresses modern while stuffed ones feel more medieval fantasy. A taste thing I guess.
I don't follow what you said about mechanisms. They are so abstracted to be essentially magical links.
As for "sleeping faster", I think that's probably more a matter of conceptualization. Surely you've had some places you've slept that are more restful than others. Maybe you took longer to get comfortable enough to actually start sleeping, or you didn't sleep as deeply? This would be abstracting that tossing and turning phase down a bit.
The alternative to "sleeping faster" would be sleeping to a lower maximum amount of rest. That is, you only sleep to 20% fatigue, and have to go to sleep again sooner, but, from a gameplay perspective, Toady doesn't want there to be more breaks than there already are, as it interferes with the rest of gameplay.
Of course the quality of bed influences the quality of sleep up to a point. It just seems like an oddly artificial bonus, I'm not even dead set against, just uneasy. One possible repercussion might be that people with better beds are less vulnerable to vampires; I'm not sure how they pick their targets. A similar mechanic might be possible with magic or even the effect of a biome. If we are to be upgrading beds as crafters level up a better system for replacing them would be nice.
From a narrative point of view insomnia might be interesting in it's own right. They may not have Advil, but coffee and tea are possible.