Sadly, similar stuff does happen even when you have more parties.

In my opinion, what's happening here is that the policies of the parties do not align with the opinions of the public. If you care about not doing a genocide, there wasn't a candidate to vote for last cycle. If you care about universal health care, there wasn't a candidate to vote for. And so on.

And you can measure this. Research has been carried out into the congruence between policy and public opinion in the US. For example, in the paper Testing Theories of American Politics: Elites, Interest Groups, and Average Citizens, it was found that the impact the average American (as a group) has on policy is miniscule compared to the influence of economic elites. You and I don't benefit from invading Iran, but the owning class sure does, so that's what we do. All this is independent of who's in charge.

And so now you might rightly theorize that since there are only two parties, the democrats can fully cater to billionaires, as long as they're less bad than the republicans. And as time goes on they move further and further right, since they really don't have to care about voters, because the only other party consists of actual demons, and people will vote for them anyway.

However, you see this effect (the wealthy having a disproportionate amount of influence on policy) in pluralistic systems as well. Norway has about 9 major political parties, yet the study Affluence and Influence in a Social Democracy finds that here too, the rich have an outsized influence. Similar studies exist for other western European countries, most of which (if not all) have more than two major parties.

So I don't think the root of the problem is the two party system (although I'm sure it doesn't help).