Sheesh. try not to let logic or rationality get in the way of self righteous arguments.
As excessive quantities of domestic animals evidently come from somewhere, we can safely assume that somewhere is most likely to be entire parent animals. Right? Whether we research or not, it is a basic fact of science and nature.
So, effectively sterilising those entire animals will reduce the potential for the production of offspring, so beginning a reduction in population numbers. If they are not bred, they cannot be discarded.
The key word here is effective. The sterilisation of entire animals has to be at such a high percentage that breeding activities are actually slowed or ceased.
I have no idea of the extent of your research Anne, but a prime example of an effective sterilisation program upong population reduction and control was undertaken by the North Carolina group "Outer Banks Spay/Neuter Fund" program called TNR (Trap-Neuter-Return - try googling that one for some initial research) which began in 1994 in an attempt to control a feral cat population.
This program was opposed and condemmed by groups such as the SPCA, HSUS and PETA alike.
The proponents of that program persevered, and TNR is now successfully used to reduce feral cat numbers, and reduce feral cat destructions in many areas.
So if effective sterilsation programs can have a direct effect on the numbers of unwanted animals breeding and being destroyed in a feral population, imagine how well they could work if effectively implemented into a population under human control, which further controls breeding behaviour!
If the originators of TNR had said "But desexing isn't part of the answer, more desexing does not contribute to the production of less unwanted animals" etc etc would those programs have ever had a chance to succeed??
Increased sterilisation of non-breeding animals is one piece of the puzzle in reducing the next generation of unwanted domestic animals. It just needs to be implemented at a level that makes it effective in creating that reduction. Making it more and more accessible is one way of increasing it's potential effectiveness.
Saying "I can't", "It won't work" etc etc, never solved anything.
As for objecting to what your taxes fund, you can go your hardest. I object to my taxes being used to house and provide for recidivist paedolphiles and mass murderers in the justice system, or subsidising methadone for recovering addicts. But I haven't yet seen a little box on my tax forms that lets me tick for where and when that money gets spent. It will get spent where is has to be spent, whether we like it or not.