Wow.  You're wrong about just about everything, aren't you?

Cats haven't "adapted" to the North American environment.  If they had you wouldn't need to feed, shelter, vaccinate or "manage" their reproduction.  They're domesticated animals.  Felis catus isn't "adapting", they're destabilizing the environment through spreading novel diseases and eliminating prey species on which native predators depend.

As for TNR working to reduce feral cat populations, by all means, provide ONE example of attrition of an unconfined feral cat colony anywhere in the WORLD since the practice was first developed sixty years ago.  Never mind--it's sufficient to point out that this worthless practice was invented in the UK, and that despite six decades of TNR, the UK stray and feral cat population has more than DOUBLED--from 4.1 million in 1965 to 9.1 million today.

Is that what you meant by "works to reduce the population"?  Which population?  Cats, or everything else?