No one said driver ants. Good old US ants and beetles can be found in your backyard. I don't use ants but I have a good population of native beetles that will clean skulls just a few feet in my woods. They are not the exotic variety that museums and professional taxidermists use, but they get the job done. I was thinking about setting up a colony in my barn, but I don't want to deal with them in the winter. They require constant feeding. The beetles do not eat flesh, its the larva that do. They don't fly until its over a certain temp 80 something, I cant remember the exact temp, so you can keep them in plastic containers. You need to skin the "parts" before you let the beetles get at them. They do not eat skin. You should also put a screen on top of the container, if you keep them inside. You do not want flies getting in because it will stink.
One of the worst killers of native songbirds is invasive bird species. The European house sparrow kills blue birds at an alarming rate. I have found more headless blue birds on my property than I can count. I have researched it, and found that the invasive sparrow from Europe will destroy entire populations of native songbirds. The sparrow pecks the heads of the native blue bird, that instinctively protects its young by shieling them with its wings, until its dead, then the sparrow makes a nest on top of the dead blue bird family. Both the male and female invasive European house sparrow will kill the native birds. This happens in bird boxes across the country. It happens at such an alarming rate that it was recommended to reduce the opening size of your birdbox so the bigger invasive species won't kill the native species for the nest.
The Starling is equally guilty of killing native birds. They are much more easily identified as they are the only black bird with a yellow beak in North America. Juveniles are greyish brown with black beaks. Unfortunately the house sparrow looks like several native bird species, so identification if difficult at a distance.
I am not a birder or granola cruncher, I was just trying to figure out what was killing the native birds around my house. My declawed indoor cat doesn't eat the heads off of birds, nor does my Rottweiler care about birds. The Rott will unstack a cord of wood in ten minutes to get at a mouse nest though.
The main point of this post. If your cat isn't killing invasive European bird species, you should be doing that. Native bird species will love you for that.