Why is baseball the only major sport where the 2 teams don't shake hands after the game?

I've seen coaches shake hands prior to baseball games; does that count? Afterward wouldn't make much sense being that the players are all over the place. Expecting everyone to gather together for a friendly "atta boy" on the pitcher's mound would be kind of silly. A lot of the players will visit the opposing team players while landing on base. Look at Orlando Hudson for example. He greets opposing players and umpires every chance he gets.