I think it’s better if you don’t ask “why were other parties unable to stake out a position?” but “how were the two parties able to claim such broad swaths of the political landscape?” No easy answers here of course, it’s one of the largest questions in political history.

I think the electoral systems, more so first past the post than presidentialism, come into it, but they’re not the main factor. Most of it comes down to America’s, all together now, material conditions.

As @cushbomb has been noting a lot recently, America’s wealth of wide open land which you could keep settling allowed potential labour unrest to be diffused. There was always more to get.

So you don’t end up with a Labour party, and around the time other countries did, America was going through the progressive era, which both parties were flirting with. The Socialists and Communists were repressed, so they couldn’t be the left alternative either.

The Progressive Party probably came the closest of anyone to breaking the GOP-Dem dynamic but honestly if they did they probably would have supplanted one of those parties entirely, just as the Republicans supplanted the Whigs, so it would have just been another 2 party system.