One reason is Givental's conjecture, which says that in the semisimple case, genus 0 GW invariants determine higher genus GW invariants. See [this paper][1] of Teleman, in which the conjecture is proved.

The theory of Frobenius manifolds in general is quite complicated. I guess semisimple Frobenius manifolds form a relatively tractable set of examples.



[1]: http://arxiv.org/abs/0712.0160