Rebound properties are one thing. Damage to the ball is another. A ball hits the bat potentially 270 times in a 45 over game. I've just looked to see that the average lifespan of a baseball is approx 7 pitches. There seems to be around 150 pitches thrown per team in baseball, as we know in baseball there are plenty that aren't struck by a bat, just like in cricket.
I'd speculate with some confidence that a composite bat does more damage than a wood one, this doesn't appear to matter is baseball as the nature of baseball means there are far fewer deliveries per ball.
A baseball doesn't hit a hard wicket between leaving the hand of the pitcher and getting to the batter like it does in cricket.
In the major league they might be constantly replaced, but not at amateur level.
Baseball's tend to discolour due to the clay, that's why they're replaced.
A composite bat still has a completely wooden face. It's only the handle and the core that are reinforced to prevent breakage. It's basically a completely wooden bat with a hole drilled down the middle. A lot of composites its totally impossible to tell the difference.