Of course they should. What FEMA shouldn’t be doing is funding the rebuilding of homes in highly vulnerable flood areas.
When I first started working with FEMA, the maximum award for Individual Assistance disaster assistance was $5000. If you owned your home and it could be made safe, sanitary, and secure for up to $5000, that was your award. If not, you received up to $5000 for rental assistance. The maximum for owners and renters was kind of the same. When I left, the maximum award for owners generally was $25,000 ($10k for real property, $15k for personal property) with no requirement that the award be sufficient to make your home liveable. Awards were the government contribution for uninsured losses. The mission changed.
In general, I think the real mission was and is to pump enough money into disaster areas that the impact of the disasters isn't permanent. There are complex rules & processes in place to determine eligibility for individual awards, with flood insurance requirements added for awards made for damages in certain flood zones. The contracts for inspection contracting firms was in the many hundreds of millions of dollars 20 years ago. I suspect it's more now. I still think the most efficient way to provide assistance would be to dump pallets of cash from C-130s. It's incredibly expensive to administer disaster assistance programs.
Much of the money spent on disaster assistance is given to states and localities for repairs to roads & other infrastructure. Assistance to individuals gets widely publicized, but public assistance is probably more helpful to regions in limiting the long term impact on their economic health. Florida will need all they can get.