Your post was fine and I thought well stated.
The problem is they are doing too well with no natural predators to keep the population in balance. There are so many that there is not enough room in the trees at night where they prefer to be to be safe and burrow under pool decks, patios and anyplace else they can think of.
The population doubles every year when there is no freezing weather lasting several days. Breeding season is still once a year late in the year and nesting begins in mid March to mid April. Gravid iguanas return to the place they hatched to dig new nests. My yard was once one of these places. A dozen or more nests would be created so many in fact the ground would collapse when I walked over it. Only in Florida do we see newborn hatchlings every month of the year. This is not normal.
Most people that buy a home usually do some landscaping and of course Florida is no exception. People here want things like Hibiscus and other tropical plants as part of their landscape. Iguanas eat everything you want in your landscape.
A neighbor spent $2000 on new landscaping and it was gone in 3 days. Another neighbor planted a few Hibiscus, went back to the nursery for some other plants and returned in an hour. The new plants were nearly totally gone by then.
In Boca Grande an island off the West Coast of Florida A pet owner released all of his pet Spiney Tail iguanas and they added a fee to the property taxes to cover trapping them. These iguanas were eating the eggs of an endangered species of bird that only nested there.
Pet ownership in the U.S. is a free for all and needs greater control and annual fees to keep the casual ownership at bay.
I have much more to say but I think that is enough.