Yes it IS possible to build houses able to withstand a cat 3, even a cat 4 storm with minimal damage, if any at all. Such construction methods are not cheap.
Anyone who has been to Bermuda will have seen them. The older homes are built with 12" & 10" thick solid stone block. Since the 1960s 12", 10" & 8" concrete block for interior walls is used. Roofs are similarly built with hurricanes in mind. Rafters are much closer together, tied together with lath & covered with stone slate, no shingles. Most windows have closeable shutters which are on all the time.
Again these houses are not cheap to build but when a hurricane comes, you close up your house, run plenty of water, because you just know that the power is going to be lost, & you stay right at home. There are NO shelters. Evacuating anywhere is not an option.
Yes, I am well aware of recent building code improvements in FL however there is a cost attached to building better to stand up to hurricanes.