Cats are fecund in captivity but there are not a lot of places for large cats to live where they don't conflict with humans.

Cats, dogs, and many carnivores have large litters but high mortality of young animals so they are able to locally explode their population in response to the availability of food. Thus if you feed them you can get a lot of them quickly.

Let’s remember that “conflict with humans” means “will eat your children.”

Depends on size. Tigers normally hunt and kill buffalo; there's no reason for them to prefer hunting human children to hunting adults.

https://www.nytimes.com/2015/08/05/opinion/in-zimbabwe-we-do...

More humans live in Cages Than the Wild.

While that is certainly true, compare this comic strip:

http://www.sinfest.net/view.php?date=2003-09-01

Or this one:

http://www.sinfest.net/view.php?date=2010-04-07

More ants live in anthills than in the wild.

There used to be more humans in the wild, though not as many as there were in civilization.

And the historical record is clear that almost everyone who experienced the barbarian nomad lifestyle thought it was vastly superior to the civilized one. But force of numbers was enough for the civilized to defeat the uncivilized, make them stop raiding all the time, take their lands, possibly wipe them out, etc. etc.