I'm not sure what you mean by "natural surface".

Do you mean leave the rails (or ballast) in place? Or, do you mean remove the rails and ballast and leave what's left, which would end up being a muddy mess?

Typically rail trails are only paved in more "urban" areas, and in the boonies they're surfaced with crushed limestone or some similar material. That certainly isn't a blanket statement, as there are exceptions.

The logic of paving in urban areas is to make the trail more user-friendly. Pavement allows older trail users--especially those with mobility issues--to safely walk on a smooth, uniform surface. People can in-line skate, push baby strollers, etc.

In more rural areas it's typically hikers, mountain bikers, or equestrians (where that's allowed).

While I also do not particularly like paved trails in rural areas, the opportunity to allow more people to use the trail is much more important than my opinion.