I don't see a point in having a new game+ run. It would be exactly like the other runs but you start with a propeller. There is no new strategy I can see to separate it.

Also useless for things like noTools. And yeah no new startegies runs would be the exact same but 6-9 seconds faster since no propeller, and some other categories like any% would barely see a time reduction, however I'd say for any% maybe we can make a case to have a noReset, but it be a meme run and just any%

I think a NG+/NoReset Any% category could be good, to bring a speedrun's goal to the logical extreme. To see how low we could get the timer. I would say it should probably be in the Meme section of the leaderboard, as I agree that it doesn't really bring anything new to the table and it would be generally just "less serious" I feel.