They gum up internall due to unburned fuel not burning off
Engine tune plays a big part. The o2 is injected to increase the efficiency of the cats and burn off that unburned fuel mixture. They need to be hot for this to work, so the o2 injection helps with this.
Ththe reason modern cars don’t use air pumps is actually two reasons. #1, cat design is more efficient, and #2 is the engines burn cleaner and without excess fuel.
So eliminating the air pump isn’t an instant death sentence of your air/fuel mixture is not overly rich.