Yeah, in TPM (Just re-watched the duel), Obi-Wan does spin a lot, with a flip here and there. But, they aren't moves we don't see in the OT, necessarily. We just see much less of it in the OT. Obi-Wan even spins in ANH, at least once.
It's AotC where it really looks kind of awkward. Obi-Wan spins almost every move in his duel with Dooku. In a 30 second fight, he spins 6 or 7 times. So that is pretty ridiculous.

Stuff like that would be really hard to cut, though. Unless you just have Obi-Wan get destroyed by Dooku right away, haha.