I'm actually a fan of having different limits for cards if the game is designed around it. I wouldn't mind a system where your deck could have say 30 basic cards, 20 special cards, and 10 super cards.
Well if there is a cost system and your careful with card design, limitations of cards like this are unnecessary.
The thing is, limitations like this can actually function very well as costs by themselves, or as an addition to another cost system. Limiting the number of certain cards that can be included can also make the game more fun.
This is one of the reasons people play the Commander variant of Magic - fewer identical cards increases the variance of gameplay. Your next game will probably be very different from the last one because you are drawing different cards.
However, this has a potential downside - the player who draws more of their powerful but restricted cards is more likely to win. But this also gives the losing player a good excuse for losing, so it can still encourage more fun.
A slightly different idea is a point limitation system instead. I've played a weird Japanese arcade only(!) card game called Lord of Vermilion. You made a party of about 5 creatures of different power levels that cost different amounts of points. The stronger ones cost more points than the weaker ones. You could put whatever characters you wanted in your party as long as their total cost was within the limit.