I can understand people having an ideological problem with F2P as it exists. There's no real arguing against that. From a functional standpoint, however, PvZ2 is just about the least obstructive F2P model available. You earn a ton of in-game currency through normal play; I have $21,000 in coins after playing maybe 30-35 levels, and powerups are 800 to 1200 coins a pop (I haven't purchased any so far; any wipes on levels just means I need to adapt my plant setup and build order).
And for folks who would rather just "buy" the game outright and not worry about the individual plant unlocks...would $15 or $20 be okay? Because here are the six plants available in the store:
Jalapeno: $3
Torchwood: $4
Snow Pea: $4
Squash: $3
Power Lily (new, this creates one Plant Food powerup): $3
Imitater (this is new, AFAIK, and it mimics any other plant): $3
So if you were staunch about having the plants from the original game, you can "buy" the game from the F2P "demo" for $14. Or if you want to just buy all of the optional plants, you can "buy" the game for $20. Granted, this is much, much more than the original PvZ on iOS (I remember buying PvZ1 for $2.99), but if you have some kind of mental block about it, the game is fully purchasable.
I don't know about balance completely, as I'm only on the second world, but the new plant types that are completely free and given to you in-game as you progress seem to give you just as many options for loadouts. And the star challenges really go a long way to forcing you out of any "I'm only taking these six plants for every single level" mentality, or at least the more compelling ones do. I almost always used potato mines (the single-use instakill plants that take a while to sprout), but if the challenge parameters require you to not lose a single plant, then using that plant will end the level once it dies off.
I think anyone who liked the first game owes it to themselves to at least try PvZ2 (it's free, anyway), run through the first set of 11 Egypt levels, and then start going through the challenges that you need to unlock the second world of levels. Give yourself an hour to try it and decide for yourself.
The bolded is the crux of the problem. Not so much from a playing the game perspective, but from a designing the game perspective.
A traditional game where you pay up front for the entire game is going to be designed from the perspective of delivering the player with the best experience possible. An appropriate challenge at an appropriate pace, balanced by the designer so that things are earned in the right order, at the right time, for the right amount of effort. (Granted, there are plenty of examples where this is done badly, but that doesn't change the original intent.)
A F2P game like PvZ2, on the other hand, is designed to take the above philosophy and turn it on its ear, so that rather than delivering the player the best experience they can out of the box, the designers build the game to tease the player with that experience, locking the things the player wants behind a price tag. Rather than having a game where resources are designed to offer a good play experience, they're designed such that the free resources offer a sub-optimal experience, with the (sometimes) optimal or (more commonly) way beyond optimal experience being right there at the player's fingertips for a small fee.
It's almost impossible to play a F2P game designed this way as an optimally-designed experience and even if it is possible, determining that balance is incumbent on the player to figure out ahead of time - a level of metagaming that renders the original game designer obsolete.
At the end of the day, these F2P games aren't really designed to be games. They're designed to be advertisements with built-in storefronts.