I don't believe it should necessarily be, but it shouldn't be some federal OBLIGATION either. You raise good point though, in 1901(?) when Galveston was completely obliterated by a hurricane, there was no federal relief, they never got a dime from the federal government to help with the disaster, and there was no FEMA. The people of the state of Texas rebuilt the town themselves, with their own resources. Galveston survived and is still alive and kicking today, proving the federal government wasn't needed.
Katrina is where things changed, and it was almost 'slight-of-hand' how it happened. Before Katrina, it had been the routine for the state to assist government help, and then the feds responded. FEMA was never designed or intended to be a "first responder" in case of emergency, that is the state and local government's role... it always has been. But because the Bush Administration was completely inept at handling public relations, they allowed liberals to distort and twist the role of FEMA and the Feds into this fucked up notion that they were supposed to BE THERE when all hell broke loose to save the people, and it was Bush's fault they weren't! Now, it seems to be 'conventional wisdom' that this is FEMAs role, and we just roll along accepting that idea, which was NEVER established by Congress or the states. It's essentially a federal power grab by liberals, which no one has the balls to call them on!