Perhaps one of the main points of blitz is to find out "when to think" during a game. If you're spending a minute on each and every move, then you're not planning correctly, and ultimately doing it wrong.
You take time to think when:
1. You've yet to come up with a plan.
2. The position is complicated and requires calculation
You shouldn't (ideally) take time to think when:
1. The opening is something you're confortably in.
2. You have a set plan.
3. You're winning and the finish is strait forward.
But on topic: If I remember correctly, Botvinnik didn't very much care for blitz games. I seriously doubt he was bad at them though.
Longer games compared to faster games


I think blitz is not for everyone, and bullet even less!
5min usually gives enough time for planning. 1min not so much. Half the time I see someone shun blitz chess, its usually because they spend 1-2 min on moves that should take 1-2 sec. The only way to fix that problem (i.e. learn "when to think") is to play more blitz games.
I can't play with the pressure of time at the moment. I have to look at the situation and study it for a bit before moving. It takes a bit of time for me to process what is going on. Have there been any famous players who were horrible at blitz and bullet games?