Hi, I had the same issue but only in one TV. The second one was keeping the session every time I opened Roku. I'm using Roku stick 4k (3820X) in both TVs (The one where Youtube was working good is AOC and the second one is Phillips). The solution I found was uninstalling Youtube and then installing it again.
"I'm convinced this is an issue with the Roku operating system."
Not sure why you're so convinced this is fact, because you're wrong. It's an issue with the YouTube app, full stop.
Trust me or don't, but you should be talking to YT, not Roku or this community about it because there is zero, zip, nada anyone here can do about it.
Roku OS doesn't handle your credentials at all. All it does is relay them to YT and YT deals with whether it's correct or not, and whether or not the app "saves" your login. It's got nothing to do with Roku.
