There are a lot of countries that have completely fair elections that aren't rigged at all and even ones that have pretty reasonable vote systems besides first past the post—and yet just the same single party still wins >60% of the vote in >85% of elections.
Why? Because when only one party has really substantially ruled your country for as long as anyone alive can remember, then nobody else can really say they have substantial experience with running a government. If you look at a place like Singapore, their pseudo-fascist party doesn't need to rig the vote because nobody else has ever won in the entire history of the country's existence. So the majority of people associate every single aspect of living in a modern country with the perceived competency of that party and so how could anyone ever run again them? It's just impossible for your resume to be more impressive.
In America, it's a similar situation but with two parties. Even if an individual politician here and there is an "outsider" they're still governing as part of the same two parties we've been living under for 166 years! And the Democrats have been governing for 186 years! Everyone seems to hate both parties but they at least trust them to serve more of the same and maintain vaguely the rule of law.
Stories of Greens and Libertarians winning local offices that you hear, whether true or not, is that these are kooky weirdos with no experience running a government and no idea what they're doing, so even if their stated principals are nice they don't know how to get anything done and often end up corrupt or making crazy mistakes that the big two parties don't make (by accident) because they have senior government people guiding them.
Is this all true? Probably not but it's the reputation and the mentality everyone has in this country. The Democrat and Republican binary represents all political possibilities. To be more left wing is to be more Democrat and vice versa and anyone else is a quack. The two parties have captured the American imagination so strongly that even if we had major election reforms nationwide to make it easier for third parties to win, I bet that most people would still only vote for the main two parties, at least for the first thirty years of a new system.
Americans don't even have very good impressions of multiparty systems. Everything you see in the news about countries with multiparty systems is always about Israel holding its fifth election in a year or Germany failing six times to form a coalition government and ending up with insane cabinets where the most opposed parties are sharing the government. Multiparty systems are confusing unstable chaos to American media trained eyes. The two party system is stable. It represents "the eternal peaceful transition of power" that is romanticized in the American mythos even when it is not true.
Every single criticism of the two party system is 100% correct. It's a bad system. And Americans definitely aren't going to be turning to a third party. Unfortunately.