People choose a state for domicile for a particular reason. Florida, Texas, South Dakota fall into that category because they don't have a state income tax, and don't put up major barriers to people who domicile somewhere but don't reside anywhere in particular. These states are not necessarily the ones with lowest registration fees.
People who have a permanent residence and domicile will sometimes register a vehicle out of state for one of two reasons:
1. Avoid paying sales tax on a vehicle purchase. Montana is popular for this reason. But it does not mean registration fees are low, they may be paying hundreds per year registration and corporation fees, to have avoided a $10,000 or $100,000 bite on sales tax, i.e. it is something that works best when the purchase is very expensive, and your home state sales tax exposure is very high. It may also be legal to do this in Montana, but illegal in your home state.
2. For lower annual registration fees, or to duck personal property taxes. Most of the time, there is an up front cost, so you need a big annual savings. I know that truckers in Kansas sometimes register their vehicles in Oklahoma to save on annual fees and taxes, but to do that requires payment of our 3.5% excise tax one time, so that it is several years to payout.
If you live in Florida, you are already in one of the lowest cost states for vehicle registration fees (and also no income tax). Your county might be getting you on personal property tax, but I think if you shop around, you won't find any big savings on vehicle registration.