The carts definitely cause damage and as stated it's pretty hard to quantify.
It would be great if some superintendents would chime in on a theory as to carts.
For a while I wanted to institute a firm rule that anyone who took a golf cart would agree not to turn the cart around while driving on grass. The driver could only go forward , no circles , none!
It is amazing how the damage is reduced by this small change in cart policy, if you can implement it.
The turning or twisting of the wheels rips the turf , not just compacts it . It's particularly malevolent to do circles. This also causes some impact to speed of play, as players become more cognizant of where they hit it, knowing they don't have the liberty of using the cart like an ATV in searching for the pellet.
It's amazing how the cart damage decreases when this policy is fixed., and to me is a simple policy that can reduce cart wear fairly dramatically!