FTR, I don't believe that cats are the only reason for declining bird populations . . . and have not said such. I also like cats quite a bit, they can be lovely pets. It's possible to like cats and see TNR programs as patently ridiculous. It's quite true that there are a whole variety of things causing damage to the environment. That doesn't mean that we should ignore the significant problem that feral cats create though.
The solution to the problems of invasive species is not to maintain colonies of the invasive for indefinite periods of time. Unless we're talking about cats. In which case emotions seem to matter much more than logic.
Cats are the only invasive species in the world treated in this manner (TNR). Seriously. Asian carp, the cane toad, the European rabbit, the Indian Mongoose, Feral hogs . . . this list could go on forever (we can trap, neuter, and release them all), and yet ONLY for cats does TNR even enter the conversation. I don't hate cats, just as I don't hate rabbits or hogs, but if TNR is the only humane way to deal with the problem of invasive species it's really weird that nobody's suggesting TNR for rabbits and hogs.
Cats are cute and cuddly, and make wonderful pets. TNR programs are a foolish waste of money though, that doesn't remotely begin to address the problems caused by having these large populations of alien species wandering around.
I am in complete agreement that the lack of personal responsibility by cat owners is the root cause of the problem, and would support any effort to increase this level of responsibility. One thing that I think would help significantly is if we as a society stop saying that it's OK to abandon pet cats to wander around outside every day. This feeds the myth that cats need to roam free and will be perfectly fine on their own. I suspect that it's adherence to and acceptance of this myth that causes much of the current feral cat problem in existence today.