I agree that zombies feel more powerful than plants, but I don't think it's all that bad. Being first to play creatures is quite a disadvantage, though it's definitely made up by the gravestone ability. Also, being able to play tricks last, while it's useful and is often an advantage, means that you can't protect your zombies with pump, unlike plants, which can often just take out a zombie with a trick before you can react. The team up ability is also extremely strong and can gain some great advantage when played correctly. As I said, I agree with you that there is an imbalance, just not as much as it might appear and this becomes clearer when you try to play zombies against high level plant opponents. I've heard of others complain about the chickening so maybe that one could be nerfed a bit for sure, though, to be honest, I've seen plenty of plant players be quite effective at playing around it when they see that I have 4 sun to spare.
The other thing I disagree with in this post is actually about the rate of card acquisition. While its always cool to get more cards more often, I've found that receiving less cards actually makes each individual card more impactful. This game has a very well balanced pool of cards, with many effective strategies and a surprising large percentage of the cards in the game are very playable, at least, in the current meta as far as I have seen. If we were able to get all the cards really quickly, it could potentially remove a lot of the joy of building up a collection through gameplay and reduce the length of the collection building experience, specially right now when there isn't really that much to do other than play ranked.