I could actually see something like the general moves happening - it would be, as you say, good for things like manifesting in the world of the living. Also for Shadow-fueled moves, depending on where you end up going with that. Those are things that maybe not everyone has, but everyone should probably be able to do if they want, right?
But maybe they're tied to stats? So if you have a high Shadow stat, you can spend an advance to pick up a new +Shadow move (or maybe 12+ expansion of the existing +Shadow basic move), or a high stat for the basic move that lets you interact with the world (+Quick?) lets you buy the 12+ expansion of that.
So you don't have to wait around until you've spent 5 advances to acquire these ungiven future type moves/move expansions, and the rules could even allow for you to grab one of these moves as a starting move (in place of a playbook move) if you have the stats for them.
So, say, playbooks with high +Quick are kind of all capable of doing Apparition moves, since those are actually just moves tied to Quick. Other playbooks would be able to gain those moves, but only if they picked a stat line with a particularly high Quick or brought up their Quick through advancement.
Then the playbooks could be, actually, super-specific in purpose: the Pardoner has this very specific range of moves, but he's also built around the Dead stat, so he'll be able to access the special +Dead moves. And Pardoner stat lines also tend to be good at Centered or Spiteful, so he'll probably be drawing moves from one of those stats as well.
It's a rather different design space, but I think the general moves idea ('advanced moves' instead of 'general moves'?) could actually have some legs.
Wasn't Knife and Candle doing vaguely similar to this? Where you could unlock more moves as your Shadowy or Watchful increases?