Just looked at my newest 10 levels:
Simple 011: glitchy.
Fear Palace: includes a fast move. (far not as fast as I wished it to be though)
Desert Island: timing required along with seeing past the obvious.
Wildfire: includes quick moves to get the nasty chomper where you want him to be.
Simple 012: both fast moves/glitchy.
Stumpoban: total oban, no fast moves nor glitches.
Tiny Forest: quick fingers in the beginning to make the jumps.
Deceptive Look: almost normal.
Spherework: pure puzzle with some mild quick moves to make it work.
Temple Of Buttons: you've just did it.
Magic Of The Void: no quick moves nor glitches... try it please, you'll like it.
So yeah, you're basically correct.

If I see a way to incorporate a lightning-fast move into a puzzle -- I can never resist!
