wolfmoon, the plants overall are a bit underpowered, but Peashooter is overtuned and it's this overpowered nature that makes plants appear to be balanced. This is reflected by the fact that you see 10 Peashooters every game and rarely do you see similar numbers of other plants. The takeaway from this is fairly simple. People play Peashooter almost exclusively, and even if you have deniers (the guy above me), play tendency is more indicative of the truth. And the trend is that the majority of every plant team consists of Peashooters, with very little exception.
You mentioned All-Star being great, and yes he is an amazing character. However, Chompers deal with him easily, but since people are more inclined to play Peashooters because of their overtuned multi-kill potential, Chomper doesn't get chosen, and you can pull off some good plays with All-Star. Given that, you might think Peashooter spam is a self-correcting problem since it enables All-Stars to do extremely well, but the simple fact is that playing a Peashooter is the optimal choice 90% of the time, and that is a problem.
At the end of the day you see a fairly diverse Zombie team in most games. On the Plant team, you do not. You see 10 Peashooters, 1 Cactus, and 1 Sunflower, or a variation of that. This is a health problem for the game, and it will have negative implications on the game's longevity if power is not taken from the Peashooter and redistributed amongst other Plants (who, by comparison, are weaker.)
It is fairly self-evident that Peashooter's kit is packed with too much. The Chili Bean Bomb's radius is absurd, and it gives very little cue as to where it is or how far it is on its detonation sequence. Also take into consideration Hyper. Not only is it a speed boost, but let's Peashooter jump 3x or more. The Zombie roof fighter counterpart, Foot Soldier, jumps once and that's all the ability does. But most people already know all of this.
I hope this cleared up my thought process for you.