IMO, there should be a $2000 USD tax per year on owning cats. If you do not register the cat, you get a hefty fine. Also dog catchers should be allowed to pick up cats roaming outside.
Many places have TNR programs (Trap, Neuter, Return), at the very least. Sure, that doesn't solve the problem of the existing cats killing local wildlife, but it at least ensures they won't continue to reproduce.
The problem with catching and keeping all cats (and dogs, really) is that most places just don't have the shelter space for them. Euthanasia for stray animals has become unpopular in many places (a stance I support and agree with), so it boils down to balancing how many animals you can get adopted vs. how much shelter space you have vs. how many stray animals there are out there.
In the past few years we've adopted three cats from our local SPCA shelter, that were found as strays. I wish every cat out there had the opportunity to live in a nice home without needing to kill the local wildlife for food.
Now I live in the city. No cats but rats and people walking dogs dumping on the sidewalk.
I take a suburb with cats.
Edit: of course, I don’t deny that cats kill a staggering number of birds.
I think we have much lower hanging (and more impactful) fruit than "ban even indoor-only cats because sometimes they escape".