Ok, yes, Zombies have a few ridiculous combos. Plants have their entire decks consisting of nothing but ridiculous combos.
The problem is, most well-tuned Plant decks aren't playing against the Zombie deck; they're playing against themselves. If the Plant deck works properly, it is 100% guaranteed to win, regardless of how well or how poorly the Zombie deck works. The only way for a Zombie deck to win against them is for the Zombie deck to work well and the Plant deck to perform poorly.
I'm also curious as to how an Octo Zombie got out on turn 3, and how repeatable it is. Because I do repeatedly see Plant players play Lily of the Valley on Turn 2, followed by a Doubled Mint and +2/+2 power on Turn 3, for a 5/6 plant that's going to double every turn. I regularly see Berries and Freezing decks devoted entirely to making sure that the Zombie player doesn't get to do anything all game long.
Yes, Zombies have some potent combos, if they manage to get all their cards together, but Plants have far more synergy in their theme decks, and often synergize with actual game mechanics rather than just arbitrary keywords. The only Zombie decks that even come close to that level of synergy are Sports decks, and that's really just because of how ludicrous Invulnerability is. (Personally, I think all cards that currently make a Plant or Zombie invulnerable should instead just give it Armored 2. Still very useful, but at least possible to overcome with enough work.)
I laugh at posts that claim that one instance of a powerful Zombie combo completely balances against the very repeatable power of Plants.