Aside from this being a slow game in the beginning, I could see it as being addictive, especially since I played it until the end. :/ I think more level variety would keep more people interested, but it really just is a slow game. A much more exciting version of this would be something like Balloon Tower Defense, where the levels are more interesting instead of just straight paths. The most annoying part of the game was that you didn't know where the zombies were going to come from, so if you plant your first plant before the zombie appears and it's on the wrong row, you just have to wait until you have enough sun to get another plant.
Another thing to keep people more interested would be adding deadlines that the player knows about. The deadlines I'm talking about would be like a timer for when you get a sun, so you can plan ahead more, or a timer for when a zombie is going to appear.
I realize that the goal with the ads between levels, limited arsenal, and only levels up to 2-4 all just try to push the user to downloading the game. It's pretty dramatic and kind of overkill that they have downloads for Mac, PC, Nintendo DS, Xbox, Playstation, iPhone, and iPad. Also, the ability to login via Facebook really tries to reach the absolute largest possible audience.