Are primaries democratic? Should they be?

[The Mikado]

Worth pointing out that the US Democratic Party (and, to a lesser extent, the US Republican Party, which still has several states select delegates through unelected state conventions rather than an electoral mechanism) are both vastly more democratic in candidate selection than almost any other political party anywhere. Even foreign political parties that have primaries (and there's not many of them) always restrict voting to members of the party, like the French Socialist Party does, and most foreign political parties have candidate selection mechanisms that are totally insider dominated, especially in parliamentary systems.

It is profoundly weird to me to see especially people from countries where leadership is chosen through votes by party leaders criticize American primaries for being insufficiently democratic when the Democratic and Republican Parties both give way more influence to the electorate to pick their candidates than almost any other party in the world. In most states, you don't even need to register with the party whose primary you want to vote for! I could vote in a Republican Presidential primary if I wanted to and influence a party I hate's choice for President! How insane is that.