> FPTP as in the US will always yield a two party system in the long run as thats the only way you can “win” in it.

I don't think that's true. If you simply removed the de facto state endorsement of parties - if you only listed candidates by name on the ballot and moved to a California type open primary instead of having partisan primaries - you probably wouldn't end up with two parties like we see today.

Party primaries are a good example of this. They're also FPTP, but that hasn't lead to the emergence of two subfactions because such a thing is hard when it's not entrenched in the ballot. Instead primaries have much more loose coalitions of groups and endorsements that shift around in every election. Even in a particular election there are often more than two.

I think personalities would probably be a more dangerous thing to attach votes to than parties.

Well there are of course always tweaks, but FPTP just has those incentives and you inevitably trend towards those bad outcomes and problems.

I mean the video explains it way better than I ever could, and there are a bunch of other political systems and the maths behind them explained ELI5 style.

This is one of the more famous results in political science: Duverger's Law. It's normally phrased as "in a first past the post system, the number of effective parties tends towards two".

It's... a useful model. It turns out not to work in practice everywhere, though, as there are complicating features with geography and ideology that tend to add parties. Canada, for example, has 2 and a half effective parties (Liberal, Conservative, NDP) in general, and more in Québec. The UK also has two and a half (Con, Lab, Lib Dem) plus powerful Scottish and Welsh nationalist parties, plus an entirely different party system in Northern Ireland. So 'tends towards' is going a lot of work.

I think we start seeing that in the U.S. with younger congress members not being satisfied with lumping them all together with more traditional politicians. Who knows, maybe we will get that here too.

EDIT: Also, if the system tries to equalize at two parties, why we do not see a similar process inside parties themselves?

If the parties have stable factions and their internal elections are FPTP, then sure. The two right-wing factions of the British Labour party just rolled over the party's left-wing by running a joint slate of candidates while the left slates split the vote.

Having said that, electoral politics within parties doesn't tend to be as important as other things: bureaucratic control of the party machinery, for example.