Under belly fabric necessary?

“why did they only cover the fresh water tank area and not the whole under belly?“

Saved money. How many look under an RV before buying a new unit?

Presumably, only that area was at risk from water and rodents.

It might also be a way to protect the fresh water tank from colder air.

If it was to prevent rodent and water intrusion why did they only cover the fresh water tank area and not the whole under belly?

It helps keep rodents out of the RV plus prevents water intrusion as you head down the road on wet days.

Probably a fiberglass-based fabric. We use it in its non-RV form (called "Pet D-Fence") to protect buildings and more from damage from woodpeckers, but it's also used to replace screens in screen doors because pets can't tear it up. And my guess is that it's also pretty good at keeping rodents from entering your RV from below.
Lynn