Re: What can be done against this thing on turn 4?

To be fair. The game mechanic that Zombies and Plants have different "turn" mechanisms makes this very hard to balance. Although its safe to say that by default Zombies turn order is slightly better.

The main flaw of the whole thing is the disparity of collecting cards vs. playing the side you wish to play. It is VERY VERY hard to keep up with both plants and zombies without stuffing money into it and the mixed boosters do not make this easier as well. Since zombies also have a tendency to be more combo-y you probably need more specific cards to play an efficient deck with them which eventually leads new players to playing plants. I mean why would you take the hard long road to collect your combo/synergy pieces if collecting efficient singles with plants is much more effective (one of Brainana is excellent; one of valkyrie sucks *) ?
An uneven number of zombie and plants players eventually leads to balancing towards the less favoured side to fix matchmaking.

the question is; why not just make exclusive plants/zombies boosters for each set and watch the problem fix itself? 

no. not really. At least not here. I already mentioned the concept of "bridge building cards" in an other Thread but the resonsnace was sort of weak. I´d be happy to see the thread alive tho.

Here I just wanted to say that a booster in PvZ:H has a far lower probability to contain no cards of a specific hero at all then in virtually every other tcg. simply because, assuming each class has the same amount of cards, you already have a 50/50 chance to roll your less prefered faction and of these 50% you still got "only" 70% that you can use the card in the class you want to collect cards for.

In the end 7/20 seems like a pretty bad ration to draw a card you can even use. let alone the possibility that the card is even really good.
To be honest PvZ:H does a GREAT job at not printing magma ragers but I still think there should be boosters for 100 gems that contain either 5 plants or zombie cards. Making sure at least your rare is at least in your prefered faction would develop useful metagame much faster. Which is GOOD.

However. Yes. more modes would be fun I think.

?? Anyone wanting a pack with a 100% probability of cards specific to a particular hero just needs to go into the Collection page then go to Decks, then pick that hero, then pick a deck they don't have the cards for.  It will give you the option to buy a pack for them.  Rarity and probability being what it is generally you're getting * cards that you already have, and if you are free to play then it takes forever to build up those 4xLegendary decks that the elite seem to thrive with.  But still if you are a proponent of a particular Hero you can slowly fill in the gaps you need in many cases.