It’s possible that wild animals simply are too busy trying to survive to do much about humans in a general way (the same would likely apply to domestic pets that go feral) and animals that generally benefit from the human system would have little reason to change it.

Also there is Tiananmen Square and the concentration camps, which shows exactly how ruthless humans can be towards one another.. There’s every indication that non-humans are treated exactly the same in Housepets! as they are on our world. This would presumably include traps, poisons, and shooting at wolf packs from helicopters in ’sport’.

A combination of development and intensive hunting could keep ferals at bay while similar programs towards strays or other non-humans in civilized areas would help humans keep the status quo very well.

Secondarily, I suspect that a lack of long-range planning ability coupled with taking a long-range view of abstract benefits really won’t work – and the “they’re distracted” notion has to work all the time, for centuries – which also seems unlikely unless some more active solution is involved.