The cats stay in a particular location because someone, a community cat caretaker, is feeding them in the area. They stay because of resources.
If you begin to trap and remove, other cats will move into the territory and will fill the space left by the removed cats. This is called the “vacuum effect”. The new unneutered cats integrate into the area and produce more kittens. This leads to calls for trapping and removing and the cycle continues. TNVR stops the cycle!