Ancient devices don't cease to work (unless their hardware fails, of course). They just don't get upgrades and new features (new apps, etc etc). A factory reset (or reflash) may be required to get rid of cruft, then reinstall apps from backup - but afterwards it would work.
If the postmarketOS would offer more features (mostly I think of apps) than some ancient Android, this may be a reason to replace the OS. But I really doubt it would happen. It would require a lot of effort to get anywhere close to Android 4.x ecosystem.
And I believe most users would prefer old apps (downloaded as .apks from random archive sites) to some security patches they frequently don't even know about.
Some old devices do cease to work or they start working more slowly. Apple slows down phones with old batteries, for example, even when they are plugged in. Many of todays devices also require online accounts and some completely stop working when those online services aren't available.
I'm kinda dealing with that with a modern company right now. My Ring doorbell doesn't work without Internet access and I can't get it for 7 days or so. I've got a home network setup, but no Internet. The Ring device won't even ring the bell on my house when you push the button, even though it is wired strait in... Now I'm off topic a bit.
The main reason for android phons to slow down is the storage, most of the android phones run cheap emmc chips, even some of the more high end ones. Even with a new battery and an AOSP rom, my Nexus 2012 is unusable even when I reverted to the version of android that that tablet came with, which is JB. So I don't believe that this will solve the hardware obsolescence problem.
Ancient devices don't cease to work (unless their hardware fails, of course). They just don't get upgrades and new features (new apps, etc etc). A factory reset (or reflash) may be required to get rid of cruft, then reinstall apps from backup - but afterwards it would work.
If the postmarketOS would offer more features (mostly I think of apps) than some ancient Android, this may be a reason to replace the OS. But I really doubt it would happen. It would require a lot of effort to get anywhere close to Android 4.x ecosystem.
And I believe most users would prefer old apps (downloaded as .apks from random archive sites) to some security patches they frequently don't even know about.