Beyond that there's also another issue related to the above. Because of aforementioned divisive rhetoric many people are no longer even voting for people they like or even want to win, but voting against a bogeyman of an opponent. They aren't voting for "their" side, but because they fear "the other side" winning would be catastrophically worse. I suspect very few people willing to vote in the first place would intentionally and actively "waste" their vote simply to make a point. And if you get some very small chunk of NotA then suddenly the powers that be might even claim that's an endorsement of them.
Voting third party achieves the same as your ideal without the possible perverse inverse messaging of approval.