Stats and basic moves do some particular things vs. your alternative implementation with, uh, let's call them "similar moves" customized for each character type.
- Repeatedly using stats ties related moves together. Sharp ties the "read" moves together; you know that if a given character is good at one, they're good at the other, unless they have a stat-replacement move.
- Stat-replacement moves are a shortcut way to re-color character actions; when a brainer uses Unnatural Lust Transfixion, you know she's seducing people with her creepy brain powers, and one supposes that the player's expected to portray accordingly.
- They allow the MC to come up with relevant custom moves for threats. In your system, I'm not sure how that would work really.
Given that, maybe poke around at some of the ideas in Knife & Candle, regarding modifying the basic moves based on what the characters are or are doing. I personally find it to be an interesting middle ground between 'custom moves for everyone' and 'all moves are the same'.