A two-party system is fine, provided that the parties are relatively ideologically coherent and united (which is currently the case, but was not the case during the less partisan 1950s and such, where both parties were basically divided into Southern and Northern wings and party discipline was a lot less strict). Ideologically coherent and unified parties are a good thing, as is partisanship, as they make the consequences of elections more clear and allow voters to make better informed choices.
The problem with our current political system, what makes it so dysfunctional, is not partisanship or a lack of collegiality between the parties. The problems are the filibuster in the Senate and unequal representation in the House and Senate, which prevent a party that wins a majority of the vote from implementing its agenda, so that the voters are able to ratify it or reject it in the next election.
THIS.
But FPTP/two-party systems prevent ideological coherence through artificially limiting the spectrum of parties. It's basically a high electoral threshold that forces people to channel their energy within one of the parties rather than letting them be free to create their own party and campaign for their platform and ideas. That seems like a conservative system designed to protect the incumbents, not an ideal electoral system that best represents the electorate.
The 70-90% one-party majorities we see in a lot of the state legislatures here in the U.S are pretty fake when you think about it.