Will we rebuild Houston? Yes. Just like we rebuilt New Orleans, many parts of New Orleans that are not rebuilt, I can imagine there will many parts of Houston that never get rebuilt.
If Miami gets wrecked, will we rebuild it? Yes.
However, think about "Littlevile". This is an imagined small town on the coast. It could be in any of the coastal states.
Let's imagine for a moment that Irma smacks Florida, as a category 3 or 4 it runs into this small town on the coast and wrecks 85% of its structures.
FEMA and flood insurance comes in and Littleville starts to get back on it's feet. Let's imagine it the whole process takes 2 years..
Now imagine at the 1.5 year mark, another storm comes in and undoes a portion of the work. FEMA has to come in again and the flood insurance pays out for some more stuff. Plus private business insurance has to pay out again for the businesses that were damaged.
Now imagine this process happening in fair number of small towns across the southern region.
At some point, it's not that the federal government will abandon this areas, it's that the insurance companies will. This will cause a cascade effect.
Sure, you'll be able to build there, but flood insurance will be so insanely expensive (imagine 5k per month) as to deter anybody from building on the coast. When this happened with Sandy that did this sort of thing, and congress howled, but at at some point after they've had to past their Nth number of relief bill that's pouring money into the flood insurance market to shore it up, the writing will be on the wall and the resistance to high flood premiums will melt away.
So imagine any set of these towns that's through their 5th or 6th partial rebuild. No businesses will be able to get flood/business insurance. What few houses are there will be mansions build on high pilings surrounded by levies.
With each storm, more and more of the residences of these towns are forced by economic conditions to move. At some point the local government bereft of a tax base dwindles to a skeleton of what it was. Eventually these small towns will have to band together for schools, fire, police, etc. These structures will become the only safe places in a storm. Built on high foundations, surrounded by levies, generators and water systems on the roof. Designed to be islands for weeks at a time. What few people remain will find the only way they can build will be to build near these regional storm shelters as zoning rules and insurance restrictions will limit them.
As more storms continue to roll in, there will come a point where the state governments will balk at rebuilding anything. Who needs to fix the pot holes in a town with no people? Why would a government issue bonds to build infrastructure that won't even last a fraction of it's intended life? While all this time, the sea level continues to creep higher and higher. Municipal water systems will salinate, as they are right now in Florida. Sewer systems that were designed when the sea level was lower will inundated as they are now in Florida. There will be no will, people or money to fix these.
There might be people who'll come out in say it, but in most cases what will happen is that legislatures in these states will simply drag their feet. When presented with the mounting costs will kneed their hands... and frankly as these regions empty of people their constituents will be pressuring them to spend money on infrastructure inland. Sleepy cities in the middle and northern parts of these states will suddenly have an influx of people, flush with money to build houses. They'll want bigger schools for their kids, these towns will need more fire / police / hospitals.
The south coast won't die with a bang, but it will die with a steady ebbing of it's people in resources.
NASA will release pictures showing a timelapse of the lights going out on the southern coasts except for the major cities where they'll be spending billions to buttress and build what will eventually become islands in a region of darkness.