Even the studies most friendly to your position put the conglomerate that cats are counted it in 4th place - e.g.:
- Habitat Loss & Degradation (40-50%)
- Climate Change (20-30%)
- Pesticides & Chemical Pollution (10-15%)
- Predation by Domestic & Invasive Species (5-10%)
- Collisions (5-10%)
- Disease & Parasites (1-5%)
- Illegal Hunting & Trapping (1-3%)
- Light Pollution (<1-2%)
Let's be very generous and concede cats could contribute 5% (sorry magpies, crows, etc pp. - you contribte almost nothing)
I don't argue this point because I am way to fond of cats. I don't even agree with the above scale - at least when it comes to (formerly) common birds such as house sparrow (Passer domesticus) and common blackbird (Turdus merula). Their main problems are Usutu virus and loss of insect biomass.
I am shit-scared about the loss of insect biomass. I am old and observant enough to have recognized the Windshield phenomenon by myself. I concur with the Danish study hinting at a 80% decrease from 1997 until 2017 (I actually think it is higher now). I live in major city with nice parks - the decrease is observable here too.
If the food supply of songbirds has declined by at least 80% that is your biggest problem right there - and it does not only affect songbirds and not only insectivores.
Over-emphasizing cats in this situation is a smoke screen/ red herring akin to BP pushing the carbon footprint of the common man.