In my "experiment" tank, those snails never know what to expect. One minute I'm feeding them, then next minute .. "smashy smashy". I always try to make it quick, a solid whack to make sure the shell crushes instantly.
I used to dislike snails but now I watch them do their thing and they serve a purpose in keeping a planted tank in balance. I find that the small ones don't hold my interest as much as the bigger ones.
Depending on the betta's personality, they could range from completely ignoring the snail to providing entertainment for them.
For me, when my Saffron has had enough to eat, he'll usually grab the next pellet hold it in his mouth for a couple seconds and then spit it out and swim away. Early in the morning when I'm headed to work, I don't have to worry about fishing out that pellet because I know the snail will take care of it for me.
Whether you keep them in your tank or not is your choice, but as long as you keep a clean tank, you don't have to worry about overpopulation.