When carts were first introduced - back when golfers were accustomed to playing on fairways that were as likely to be hardpan as grass - this wasn't such a big deal.
Today, though, advances in agronomy and turfgrass management have introduced great varieties of grasses to areas where they weren't, in the past, able to grow.
As a result, courses are in better shape than ever. But another result is that many of these turfs are more responsive to wear and tear.
And driving a cart over these grasses creates far more wear and tear than walking on those grasses or pulling a bag cart over those grasses.
This is one reason why many courses post the 90-degree rule for riding carts on a permanent bases. Riding carts are often not allowed off the cart paths following periods of rain. Some courses no longer allow riding carts on the fairways at all.
Walking a golf course is a good thing to do for the sake of the course itself - it saves wear-and-tear and damage to sensitive areas, which creates a better golfing environment.

