The ones that don't are: Kyra (she does, but very selective), Sajan (also limited recharging), Valeros, and Ezren, while Seelah has one that is a wildcard as it takes the top card of the deck, which could be good.
Also, even if you can discard or recharge cards, it is not unlimited, you can still end up with a lot of junk in your hand that limits what you can do.