Canteens won't have as big of an impact in gameplay as non-stock weapons. For example, the Soldier won't be able to use his banners or have access to the Beggar's Bazooka, which neuters his supportive and offensive capabilities in MvM. For other classes, like Heavy, there won't be a major impact on how he's played. I'd say it should be fine to have canteens in stock-only.

I agree that having these categories would be interesting. The SR + Kritz Med combo makes the game way too easy, speedrunning or otherwise. Having all stock weapons would be interesting as well, since it's the closest thing to starting off from a new profile, but with more experience as to speedrun with stock combinations, rather than the meta that we've established.