Ever heard of a dog or cat with fertility problems? Must be very rare.

It happens as it does with humans, it’s just not often noticed unless the animals are being deliberately bred.
As a teenager I was involved in the whole dog show thing, and there were some serious fertility issues with some of the breeds that had been severely line-bred, and some required a fair amount of help to reproduce. It was kept fairly quiet, as that was considered a flaw, but it was really quite prevalent.

every sterilised one.
not rare at all.
in fact, finding one without fertility problems is rare.