IIRC the band was trying to represent a Mod hopped up on pills, hence the stutter. I don't have a source for that right now.1967
The BBC refused to play The Who's "My Generation", saying they did not want to offend people who stuttered.
Two other Who songs also were banned: I'm a Boy (cross-dressing) and Pictures of Lily (masturbation).
Postscript: So sad to see a young, exuberant Keith Moon.