What is the use of manifold learning?

Sorry for the provokative title, but we were discussing manifold learning at work, and I can't quite work out when you'd use it, and why.

Given the difficulties standard manifold learning techniques have with unwrapping or flattening T shapes where two surfaces intersect (like _|_ ), and closed surfaces (like the surface of a ball), why do people use manifold learning instead of just finding connected subspaces in the original feature space?

I get that visualisation is the killer app for manifold learning, but are there any other benefits in unrolling your data into a plane, or into a 3-space?