FEMA's responsibilities shouldn't be handed over to states because the disaster response would vary greatly. States such as New York, Illinois, Florida and California would have better disaster responses because they have higher populations and more tax revenue. By contrast, if a hurricane decimates Louisiana, Alabama or Mississippi, the response would be much worse because of less tax revenue. FEMA should be a federal agency so it can help where ever a disaster strikes that state and local governments can't handle.
Giving FEMA responsibilities to the states could potentially create a lot of problems. First, there is the issue of how FEMA's funds would be divided since there is really no way to anticipate when and where disasters happen. Second, there is the issue of how each state would define a disaster or delegate FEMA funds. What some states consider worthy of FEMA funds, others may not.