wonder if grinding up birth control pills and mixing them into food the mice can steal would decrease the chance of mice reproducing in my house

this is an extremely silly idea but I am in perhaps the optimal conditions to try it:

1. mice keep getting into this house
2. they are much too good at evading traps
3. they will eat poison but I prefer not to feed them poison bc I might adopt a cat at some point and I don’t want to poison the cat (or other local predators honestly)
4. I actually have a lot of birth control pills that are old enough I don’t trust their reliability for human use (my prescription kept refilling for quite a while after I stopped taking them because I realized I don’t even mostly like doing the kind of stuff that causes pregnancy)
5. I strongly suspect they work on mice, because very few medicines ever get to the point of being used on humans if they don’t pass the test of “does this work on mice”