I've done a ton of testing, but have not found anything that eliminates the stutter. The consistent behavior is that if I open up enough apps to cross some threshold (like filling up the RAM), the stutter starts to occur.
I did a fresh install of iOS 14.2, setting up as new and not restoring from backup. I started just by opening and closing all the pre-installed apps, and saw no issue. Then I installed a bunch of new apps, opened and closed them, and started seeing the stutter. Then I deleted those apps and installed a bunch of different apps, opened and closed them, and saw the stutter again. So it seems to not be a question of *which* apps are installed.
I did another reinstall of 14.2, this time restoring from the encrypted backup. Opened and closed a couple dozen apps, and started to see the stutter.
Installed the iOS 14.3 public beta. Opened and closed a couple dozen apps, then started to see the stutter.
I've also chatted with Apple Support, but they didn't recommend trying anything I hadn't already done. They did a remote diagnostic, but didn't see any problems. Next step would be to have an Apple technician service it.
So I'm not sure what to make of all this. It certainly *feels* like a software problem, but the fact that a significant number of people say they don't have this problem makes it seem like a hardware issue. It's possible there's yet some setting I've missed which is causing this. Or maybe the people who don't have the problem just don't use the phone in the same way such that the memory (or whatever) gets filled up.
I'm kind of at a loss, and honestly a little upset I'm beyond the 14 day return window, because I don't really want to spend weeks having the phone shipped for service, or go to an Apple Store during the pandemic.