"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.
onn Roku 43" TV model 100012584 running version 12.0.0
Twenty plus years of online experience as a web developer, general user and consumer. Recording engineer. Sixty plus years of troubleshooting and problem solving in several fields. Here to help and get help when I have issues with Roku. Nothing more. Not here to socialize. That's what real life is for. 😉