I agree with you. However I think the inability of FEMA to function properly means they are not the answer.
I think FEMA is probably not the answer to a major disaster such as this that was badly handled on a local level. FEMA was never meant to be a first responder - they hand out loan and grant applications and arrange for contractors to repair damage after the event. On the other hand, it is true that we really don't have anybody delegated as coordinator of first responders, and maybe this needs to be examined.
Theoretically, the city and state in question should react first, but here we had a total breakdown in the city and state - and there was no way to take over from them without invoking the Insurrection Act (or declaring war on the state of LA, which probably wouldn't have been a great precedent!).
States' rights are very important, and the US Constitution is essentially based on a principal of subsidiarity. The lowest level acts first and solves the problem; if it can't, the problem goes on up the chain. In this case, the lowest level (city) didn't act at all, and the next link in the chain (LA) refused to act, and there is currently no constitutional way to bridge that gap and go on up the chain to the federal government.