Not all of the Democrats primaries were closed either. Obama won many states thanks to independent support that Clinton didn't get. I think the GOP's system is better than the Democrats because unlike in the Dems, one can't just win all the small caucus states and stay close in the big states and siphon off delegates. Hillary won most of the big states and the popular vote, but lost the nomination because Obama was able to fund a caucus game more efficiently.
Hillary almost certainly did not win the popular vote in primaries and caucuses where she faced Obama. Note that Obama was not on the ballot in Michigan, and agreed not to spend any money or campaign in Florida, in compliance with party rules. Also, some caucuses, such as Iowa, do not release PV numbers.
Hillary only showed up in FL on election night. And it's Obama's fault he removed his name. If even you remove MI, Hillary has more popular votes. And caucuses don't need to release popular votes. They are undemocratic. Just look at Texas, which has a primary and a caucus. Who won the primary (the voter's choice)? Who won the caucus (the establishment choice)?