How a game unfolds in a card game is very dependant on the initial hand. Essentially, the initial draw gives you a random subset of your total abilities to work with. That means your game plan changes with your draw. A lot of the work in deck construction for CCGs goes towards making that initial hand has good options for playing.
The big advantage of this is that each game is slightly different. Sometimes you'll have lots of small effects to harass your opponent. Other times you'll have to stall until you can play a big effect.
Contrast this to WoW. In WoW, you always have access to the full set of your abilities. That means that most non-raid boss fights tend to progress in the same manner. First you play ability A, then you play ability B, and so on. There's some reaction abilities like Kick or stuns, but by and large, once you have worked out a rotation, you stick with it.
(I suppose this doesn't apply to healing in a 5-man, as that is very reactive, and thus different each time.)
Imagine what gameplay would be like if a random 2/3rds of your abilities were locked out when the fight started. I think it might be pretty neat. Every fight would be slightly different. No Fireball this fight, use Frostbolt!
However, it's pretty hard to come up with a reason to justify only having access to a random subset of your abilities in non-card games. In a card game, it's just obviously the way a deck of cards works. Once you accept the metaphor that your powers are cards in the deck, you don't bat an eye at not having access to all powers at all times.
I can't really think of a way to justify not having all your abilities available for a non-card game. Why shouldn't a Warrior be able to use Mortal Strike when he has enough rage? Yet, the initial draw is a very interesting mechanic that goes a long way towards countering the repetitiveness of individual fights.