Not only wave length, but also beam width. The laser is spatially very compact. Radio waves need larger antenna apertures to be that focused. It's hard to get tight spatial resolution with a beam that looks like a balloon animal.
Also, multipath and time-of-flight is difficult with radio waves, and the EM reflectance is weirder. Light is just much more convenient for this purpose. But - it's not outside of the realm of possible.
No, compressed sensing only allows you to attempt to reconstruct the original signal from a limited subset of the data sampled in a specific way, as long as you can assume some kind of sparsity on the data in another domain.
Fundamentally, you cannot get something from compressed sensing that you wouldn't be able to otherwise normally.
Also, multipath and time-of-flight is difficult with radio waves, and the EM reflectance is weirder. Light is just much more convenient for this purpose. But - it's not outside of the realm of possible.