That video looks deliberately exagerrated - had me doubting myself so I just checked my own technique. OK, I grabbed an SS because all my other bases are cased up...
Doing one finger per fret on the first four frets my wrist is virtually straight, nothing like the video. Also, my hand only moves about 1/4" between fretting 1 and 4. One point of 1 per fret is that your hand hardly moves when playing across the neck.
I think he's exaggerating to prove his point.
All I can say - I'm glad I've got big hands!