Composite baseball bats are specifically designed and tested to ensure they have the exact same rebound properties as a wood bat. They're just considerably more durable. Whereas the professionals use wood bats, amateurs typically use composite (they're more expensive - £150ish vs £80ish but they do last 5 times as long so its worth it).No reason they couldn't design an composite cricket bat for amateur cricket in the same way.https://thebatnerds.com/what-is-bbcor/
Is there in game checks?
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.