It might be interesting to think in terms of "what would cause the machine to be saved?"
With something like an original XT-class machine, there were a lot of timing-sensitive programs that, frankly, the turbo switch wouldn't quite fix. You also had the fairly significant differences between XT and AT hardware on things like hard drive controllers, so you might be more prone to keep the old machine around in case you needed some data on it.
Conversely, there was relatively little a 286 could do that a 386 or 486 couldn't do just as well. There were a few pieces of software (some early Xenix and OS/2 releases, and a few utilities, as I gather) that touched undocumented or misdocumented stuff that ended up breaking on 386s, but most people never encountered them. So you probably didn't need to hold onto the 286 just in case.
I'd expect most 286 machines were being retired for upgrades in the 1992-1995 or so range. At that point, they held enough resale value that you're going to see people trying to unload them, rather than just sliding them in the attic and waiting for them to become vintage. I wonder if that led to lower survival rates: instead of first-owners saying "I spent $5000 on it, I can't come to terms with throwing it away", you had the people buying them second hand for $300 with far less attachment to it once they got a shiny new Packard Bell 486DX2/66.
Indeed, I could see price attachment being a big part of survival. I'd be unsurprised if the survival rate on "luxury" machines-- the AT, the PS/2 50 and 60, the Deskpro 286-- was a bit higher than on no-name clone 286s, particularly late-era ones where they were clearly budget offerings to fill the bottom of a catalog promoting 386 and 486 boxes.
I can recall my family selling their first PC (a Magnavox-branded 386SX/16) in 1995. We had at least one guy say "I refurbish the machines and sell them overseas", and he said for his purposes, he preferred a 286/20 or 25 because the 386SX wasn't meaningfully faster. I suspect if you actually wanted 386-native software, it would suck on a SX/16.