First-past-the-post voting leads to a two party system which leads to more polarization. If you have multiple political parties, polarization can only go so far because there will be centrist groups working against polarization. In the US, there is no force pushing for centrism.
There is absolutely no way either political party will allow a multi-party system to ever exist.
I've suspected for a while that the real secret to getting PR/MMP (=> multiparty) in the US is getting the Catholics on board. They're sick of the Trumpists and libertarians in the Republican Party but they'll never support the vehemently pro-choice Democrats. They should be obvious fans of a multiparty movement, and they have the political and media heft to move the needle.
Alas, I'm not Christian and my views are quite a bit left of theirs, so I don't think they'll listen to me. And most PR advocates have more in common with me than with the modal Catholic American.
With any luck, these reforms can stick and hopefully expand— necessary steps if we're ever to end this political duopoly.
The result is a wobble left for awhile, then a wobble right.
However the resulting wobbling isn't much different in practice outcome-wise so far because turnout tends to depend on level of outrage which depends on how long the other side's been in power, it's had much more significant of an effect on how elections need to be fought.
(much information about this can be found by googling 'negative partisanship' or 'rachel bitecofer' +/- the word 'model', I'm not including specific links because which outlets/articles/etc. will be preferable to a given reader will likely vary so providing a guide to finding a range to select from seems more useful than my trying to select on others' behalf)
If you want a culprit, blame the lack of whipping that both US parties do as a matter of political culture. Since you have historically had all these cuckoo crazy subgroups within both parties, it has meant that other parties simply do not have the bandwidth to exist.
However, in the last four years, the Republicans have started to blindly follow their leader as a matter of pride. I see that as the one positive change the Trump era has brought; yes the man to bring it about has been a disgrace, and has used it for vile purposes, but if both parties stick to following their political platforms and leaders far more, the US can end up in a better place.
Quebec is another big difference–there is nothing really comparable in the US. Spanish is the closest thing the US has to French, but there is no state in which Spanish outranks English–and even if predominantly Spanish-speaking Puerto Rico successfully gains statehood, Puerto Rico would be only a medium-sized state in terms of population, so it will not be able to have the same impact on US national politics that Quebec has on Canadian.
The US has a lot of cultural diversity, but its cultural diversity is spread out thinly, rather than being regionally concentrated – as a result, that cultural diversity can't be reflected in the political sphere in the same way that it is in Canada or the UK or Belgium or Spain, where the distinctive culture of specific regions of the country causes them to develop their own unique party systems.
The big difference is as philistine implies: the two US parties are dramatically more democratic internally, so there is just far less need for people to create new parties to begin with. By world standards the Democrats and Republicans are barely coherent parties at all. For instance they barely have any manifesto, instead presidents have manifestos, but that's meaningless if the party members don't agree hence why shit is always being "blocked by Congress" in the USA when you rarely see that in other countries. The two US parties are more like vague semi-stable alliances of people who don't really agree on much, that happen to march under a shared flag for the sake of convenience and due to FPTP.
Another difference: an outsider who isn't even a party member or who was actually a member of the opposing party, simply cannot run in open primaries in most countries. Yet both Sanders and Trump did this. Nor can they take over the party against the will of the representatives themselves, which is what Trump did. The closest equivalent in Parliamentary systems was Corbyn, which occurred the moment the rules were loosened to allow more open voting for who leads the party, and that nearly destroyed Labour. They have now changed the rules to re-establish the power of the MPs over Party leadership.
The USA will see more parties appear and compete if/when the two big parties develop internal cohesion, for example by insisting that the party leader/president is picked by Congress alone, and in which Congress members who defy the party line are kicked out of that party. Otherwise it's kind of meaningless to try and create a new party in the USA when the existing parties don't actually stand for anything to begin with. It makes far more sense to try and take one of them over.
I don't think that's really unique to the US. That's an inherent problem with presidential systems–the President and Congress are independently elected, and so they can be controlled by different parties, and even being controlled by the same party is no guarantee they will cooperate–and presidential systems are very common in the Americas–most Latin American countries have the same system. I'd be surprised if Latin American countries don't have some of these same problems with "political gridlock" that the US does.