This natural feedback cycle has been around for millions of years, just not the human element.
So to repeat: Please keep your cats inside!
In places where cats are essentially an invasive species, not native at all, this is different of course.
And again, when bird populations reach equilibrium the cats can't find more. That's independent of cat populations.
Also, feral cats tend to congregate close to human populations.
I'm not sure what your point is about equilibriums. Of course equilibria are reached naturally, but with the human factor these equilibria have been distorted beyond any natural capacity. In short, any human-impacted equilibria tends toward the rapid decrease in species populations, often to the point of species extinction.
There may have been inter-breeding involved with wild populations, but most, if not all, feral cats have their origins in domesticated, or captive (by humans), cat populations.
Also, have you ever noticed that feral cats tend to congregate near humans? That's because they find it easier to find food from dumpsters, handouts, garbage, etc. This is very similar to other species that rely on humans for their success (rats, corn, cockroaches, crows). This artificially increases their numbers. I say "artificially" because their food source comes indirectly or directly from humans.
So simply from the definition of the word "feral", and not even including the inter-species dynamics between humans and feral cats, humans have everything to do with feral cat populations.
The feedback cycle is broken where the cats have ample food supplied and the cat population no longer depends on the prey population.
I strongly recommend this book for a deeper understanding: https://www.amazon.com/dp/B01CO34KU6/ref=dp-kindle-redirect?... There are MANY species that have gone extinct or are approaching extinction because of cats.
A bird nest has what, 4 or 6 eggs? All those hatchlings are pretty much born to die in the first year. Because next year, the bird population is pretty much the same.
Cats can only catch birds when they are plentiful. When the population is back within bounds, cats find birds hard to find. Its a natural feedback cycle, been around for millions of years.
If the cats didn't do it, then most of those birds would starve the first winter. Is that more kind?
It's nice to feel positive thoughts about birds. But don't let that poison your feelings about cats, who are only doing their job.