Why do we have pawns?
I would say that pawns do a great job of outlining your position. They can stop minor pieces and heavies from advancing down the board into your your camp. Best of all, they can be promoted at the end of the game, making the endgame a very interesting phase of the game. I do see your point that pawns can sometimes get in the way, but I do think that pawn lead to a more interesting game of chess.

What kind of war would it be without infantry? Pawns are expendible, and if used properly are the deciding factor in your game. All openings have a pawn in them, all endgames go back to how you used your pawns. Basically, pawns are the soul and blood of chess.

Chess is a war game and pawns are foot soldiers (or as batgirl wrote "cannon fodder").
Like in real life, they are usually the first to be sacrificed... :-(((
Pawns are basically defenseless and are captured easily. Sometimes pawns are the very reason we are mated. Imagine a world without pawns...