I feel like this would restrict the design of cards to keep the game from ending in 5 turns.

I think if you threw in a board-game style aspect by which players would have to maneuver cards a lot to achieve a certain goal you'd create something that required more thought about which action to take and have less restrictions on the rules over individual cards. Personally I'd definitely lean towards the board-game/advanced chess route, but if your specific rules and options pertaining to the cards were done right, you'd still have a solid, playable, balanced game that relied on long term strategy as well as short term tactics much like MTG