Like just about everything else in the hobby it comes down to what the goal of your game is.
First off, if you're a bit clever as a GM you can absolutely fill in a little bit of time where someone's one character isn't available. Hand them a relevant NPC in an encounter or story to fill in for. Give them a task to write up or do something for game management, or even solicit them for feedback and results on something. With some groups that should work fine.
In my younger days I do recall some people doing this sort of thing rudely. Not people I gamed with frequently, but occasionally I'd play with another group or a one-off person that intentionally didn't want to be a part of the game except for "their turn" or whatever. Constantly in their phone or going back to their desk to play Everquest or something. Essentially they really didn't value other people's time very much, and that's rude. Similarly later in life I had a player that despite agreeing that for this campaign we're all playing characters that are willing to flex their personality and goals a little bit so we can get things done in a limited amount of playtime, but they still insisted on building and playing characters that had their own entire subplots not-related to the game or the rest of the group at-all... and they insisted on following those plots and goals exclusively. Stuff like that is rude.
It's not that different from player elimination in a board game. If the group likes that kinda game and can deal with it and someone goes and watches TV or something when they're out of the running, totally cool. Some other games a player "feels" effectively eliminated but is still an important part of the process... I kinda feel like they should take one for the team for a bit and still at least pay attention and try.
I guess at the end of the day all I care about is "does this action show at least proper respect to other people at the table and other people's time?" Then it's fine.
