I think the main issue with this idea that "game over" is outdated, is the fact that any mechanic can be made to work in a video game when it's implemented correctly within the context of a given game. It has nothing to do with Sonic Mania being a platformer. Game overs work fine in some platformers, but not in others. Its simply a matter of how the game is designed and how the game over affects the game.
Difficulty in games is fine, and there should be some consequences for failure or it'll lose all meaning, but that can also be taken too far. I haven't played Sonic Mania so I can't say anything directly related to it specifically, but it doesn't seem to me like the game overs in it are exceedingly punishing.