Well no. The card element of trading card games is just a physical representation used in the real world so that people could manipulate the elements of the game, but there is no law dictating that shuffling cards needs to be a part of the game or that it can be the only part that depends on luck, so yes, it can be taken away. Mabinogi Duel is an example of a card game, very similar to PVZ Heroes, in fact, that does not have random drawing (you have a deck of 12 cards and you hold them all in your hand from the beginning). It is also wrong to think that luck has to be reduced to 0 to be competitive. You can read some of the articles that Mark Rosewater has written about game design to see how luck and game design can interact to make games both more enjoyable and competitive.
I don't know about the last couple of years of MTG, but last I played competitively, they were still printing cards that made you throw dice, though it's true that these where mostly more casual cards. However you are right, Hearthstone is a better, more modern, example of how a competitive game uses luck all over the place in its game design.
Anyway, you can't say that drawing cards is an integral part of card card games and that particular element needs to have luck, because that is not the case, it's just another gameplay element and thinking like that is just shutting down game design possibilities. It's important to be careful in the implementation of a luck based element for sure, but when its well executed it can be both enjoyable by the masses AND competitive.