There are two separate issues here. First, you can accept that a move should be hard to pull off -- that the right opening appears roughly once per fight or once per few fights -- without agreeing that per-encounter and daily powers are a "good" way of implementing that idea.I see daily and encounter powers as a special move which makes the hero unique and instantly identifiable. But it is also something that the hero should only be able to pull off rarely.
I put "good" in quotes, because it really depends on what criteria you care about. If you want to give the players simple but interesting choices to make, a meta-game resource works. If you want an immersive simulation, a meta-game resource makes no sense at all.
I think we understand that and even agree on it, but that doesn't mean the mechanic makes sense.The "daily" and the "encounter" limits are there to keep those moves special, and to stop the action movie becoming a boring loop of the same shot played over and over again.