It wasn't inappropriate, it's just that you typically didn't have multiple cable boxes. There wasn't really a reason to have a TV in a kids room if you're only getting OTA broadcasting, there wasn't much for kids other than like Saturday morning cartoons. I knew plenty of kids in the 90s with a video game console and TV in their room though. It was for games, not TV watching.
My parents certainly were of the opinion that it is inappropriate to let kids watch TV whenever they want to.