If I understand correctly, in the US, all citizens registered to vote must indicate a party affiliation or as an independent? And, all those with a party affiliation can vote in primaries. In the past, that may have worked fine, but in this age of such societal polarization and dependency on social media for "news" and "facts", isn't that just a recipe for producing a candidate like DJT?
In the Canadian and other British parliamentary-type systems, dues-paying party members (who have a genuine interest in politics and policy and not just a desire to extend a finger to, or blow up, the "system") choose their party leaders. The two largest parties here, the Liberals (Grits) and Conservatives (Tories) have about 300,000 and 270,000 members, respectively.
I'm not saying either system is superior to the other. While our system may be seen as more stable, the American system could be more democratic.