Don't know the stats to validate if that is true that most teams go on a run after hiring a new coach but I'll assume it to be true.
I think the reason it happens is probably because it feels like a new season again regardless of where you are in the standings. There is renewed hope, everyone starts at the ground level regardless of how things ended with the old coach. The new coach has no bias for or against you so you try harder to perhaps start off on the right note so you're not left behind as sooner or later, all coaches have their favorites and guys they rely on in key situations and if you're on the fringe, you will likely not be on the team long term in a big role.