Their "broad popularity" only ever existed in the context of US FPTP election, in the context of a two-party system. If Americans had the option to vote for e.g. greens or labour or fiscal but-not-social conservatives, neither Obama nor Trump would be as popular. But Americans don't have such options, because even though some of them are right there on the ballot, voting for anyone but the two major parties under FPTP is literally throwing your vote away.

And it's not any different in primaries. Primaries are also FPTP, with all the same mechanics. The notion that you're better off voting your heart in primaries without consideration for all the standard FPTP mechanics making your vote useless is just another lie to make Americans feel better about their broken system, and is not backed by any math.

I brought up France and Venezuela as examples because they are more analogous to the US, in that they have powerful presidencies. It was to point out that the FPTP voting system is not all; more important for balancing the people against the state is the power (or lack thereof) of a parliament or congress to check the executive branch. The US is headed in a direction wherein the congress simply rubber stamps the executive of the same party; but again, to my point about Americans preferring gridlock, this is exactly why the opposition tends to gain seats in off-year elections.

And to my point about the wide range available in primaries within each party, it's exactly why longstanding politicians lose their seats to others within their own party who are more attuned to the electorate.

I think the focus on voting systems is misguided, but in any case, it's written into the Constitution and has been this way since the 1770s, and there is zero chance, ever, that the United States will adopt a parliamentary system. So the whole thing is moot. And as interesting as it is to read the opinion of America's faults from someone from a country with only one functioning political party, where all local and party elections are determined by force / kidnapping / murdering the opposition, it's tiresome to be lectured as to which system is more successful at improving people's lives or fulfilling the electorate's demands.

I don't entirely agree.

I live in Australia which has a preferential voting system, and yet two parties dominate for the most part.

There are electoral-related reasons for this but also there are branding/marketing reasons that make it more likely that large parties continue to dominate.

It's easier for large brands (parties) to hold mind share. It's very hard for minor parties to build a brand built around anything other than opposition to specific things or outrage.