Wait, so you're advocating for pill-based animal birth control as an alternative to surgical sterilization, on the basis that subjecting animals to surgery to spay or neuter them is medieval and inhumane?

I want to make sure I'm clear on your proposal before I address it.

Edit: Your edit indicates that yes, I have your position correct. I would submit that we don't do that because it's untenable to round up every stray animal (or even any particular stray animal) and administer a birth control pill every single day. It has very little to do with cost (except in the sense that to implement such a plan would be incredibly, prohibitively expensive) and very much to do with practicality; it is far easier and far more effective to spay or neuter an animal once and then release them back to where they were than to track down, catch, administer pills that risk being ineffective if you miss a dose, and then release again, every day for the duration of the animal's life post sexual maturity.