And what was your plan, exactly? Are you calling for an end to the First Amendment? People shouldn't be allowed to assemble and express political preferences unless it's done the way you prefer? How would you enforce that, exactly?
Vote for those "unlikable" third parties, of course.
"That they won't win" is certainly one issue, as people don't like to throw their votes away. But "these people are generally loons" is the more typical rationale. Parties that are absolutely obsessed about weed, or communism, or destroying intellectual property, or disarming the military, etc., don't fail because we have a "two party system," they fail because very few rational people would ever want to give such parties control of the government.
You just described the Democrat and Republican parties. The difference between them and the typical third party, is that they have much better propaganda and much more money to throw around to spread that propaganda, hence the common but wholly delusional concern about "loons". That concern didn't stop party voters from nominating Obama or Trump, did it?
You don't need to destroy something, you need to actually create something. How is that not obvious to you?
Because it's not true. Your proposal is so highly leveraged against you that it would take immense time, political capital, and of course, huge, enduring support from the public probably over the span of decades. It's not going to happen in the face of the current powerful two party system just as it hasn't happened since the formation of the US more than two centuries ago.