I don't think it'd be very intuitive. In most games you release the button while actually in the air to cut your jump short,
Yes, and that's why I suggested "release to cancel the anticipation and get an immediate small jump" rather than "jump when button is released and use amount of time spent with button pressed while on the ground to define jump height" (that last one is very indirectl although equally dynamic).
so I would hold the button down during the anticipation (so that I could release it late in the air to cut my jump short) and always be punished with max anticipation unless I read about how it handled its jumps. It's not even something I'd figure out through normal gameplay.
I'd have hoped that "release before anticipation is complete" would be the intuitive extension of that mid-air button release. That would only work fine when non-anticipated jumps allow the player to hop over a small obstacle on the ground, like a rat or a rolling hazard. If forms of the hazard suggests that you'll be able to avoid it with just quickly lifting your feet (rather than trying to gain height), then a quick tap could be a nice complement to the "anticipated jump to grab that branch and climb up that tree.
Again, I wouldn't recommend "my" cancel approach for any platformer, but rather for action games where jumps are a secondary move required to explore other parts of the environment (thus usually anticipated, and performed after the environment was made safe enough), and where the designer wish to extend the use of that JUMP button to offer some counter moves.
The Smash Bros. series is the closest to what you're suggesting that I've seen. Each character has an "anticipation animation" of a certain length that always plays completely. If you let go of the button before the anticipation animation has finished playing, you get a shorter jump.
Not surprised her: Cancels are something that is involved in many fighter games, as their core gameplay lies in "more delay => stronger blow at the expense of longer exposition to opponent's blows".