Primaries are not elections in the strict sense - they were intended to be the internal selection process by which a party selects its candidates. They were not intended to be like some kind of early-runoff. No other country - including far more well-run democracies like Australia or Canada has anything like "primaries". Candidates and party leaders are selected either by an internal committee or by an internal election open only to card-carrying, dues-paying party members. That is how Corbyn was selected for the Labor Party leadership. Has it been some kind of "open" process in which Conservatives and LDP could have participated then Corbyn would have lost.
However what they do have that the US doesn't have is multiple viable parties.
Open primaries have their own problem in that they can be sabotaged by members of the opposing parties voting in them. So while closed primaries are bad for Sanders in this particular primary season. The shoe may be on the different foot in other election seasons.
Mostly I'd love to simply throw the whole US electoral and political system out and adopt a parliamentary system - like we would have right now if that so-called "revolution" by those aristocrats had failed 240 years ago. The US system is built around the cult of the individual instead of ideology and solidarity.