It does actually work that way, at least sometimes. If a major party loses enough votes to a third party, it forces them to adjust their platform at least enough to win back would-be voters.

Whenever third party voters honestly tell people that they are voting third party because it closely aligns with their values, and that neither major party is even slightly compatible, major party apologists and cheerleaders come out of the woodwork to saying actually you're one-of-us, you just don't know it yet, and if you just vote hard enough for my candidate then things will get better. It's been over a hundred years of least dirty of two shirts, and it's not getting better.