Pat,
The width of carts from tire to tire is right around 47". Increase this, even negligibly, and you can't transport them side by side using existing trailers.
Doing it to the 'inside' framework, suspension, rear end, etc., would require a lot of re-tooling.
There's a grass parking lot at a mall in Farmington, Ct. that uses an underground network of corrugated plastic pipes. I don't recall their exact length, but they are placed vertically in a honeycomb pattern, filled with stone, gravel/sand?, then topsoil/seed or sod is placed over the top. They use the lot for overflow during peak shopping seasons. I don't think it would work on a golf course as it's expensive, impossible for a cart to follow without some outline, and you'd still get some disruption of the surface if carts were driven over it in wet weather. It might be more effective if used to manage wear and tear in areas where carts enter or exit existing paved carts.
At Hotchkiss we used to use a very hard rubber matting that had a honeycomb pattern, similar to stuff you might see on a shower stall floor. It was colored green, was visible, and grass grew between the 'cells'. It was effective but eventually it melded into the surrounding grasses. We only used it on level areas as it could be slippery on hills.