“A closed primary won’t change that. “
So a closed primary won’t change anything, yet half the country is on an open system and half are closed. If there is no net result difference with either one then why aren’t they all closed or all open?
Obviously half the states feel there is an advantage to their system. And why don’t they change with changing times as you mentioned about how it was way back when?
The complaint one usually hears is that open presidential primaries in states Republicans will never carry give an advantage to more moderate or liberal Republicans. There's something to be said for that theory. It's also a variant of the Carter-Clinton-era complaint of liberal Democrats that the Super Tuesday primaries in Southern that Democrats usually lost hurt the more liberal contenders who were the choice of party activists.
Open primaries were a good idea when the parties weren't so ideologically divided. If there was a chance that Democrats might actually nominate the more conservative candidate, it was a good idea to be free to help that candidate win his primary. That rationale doesn't exist nowadays, but if one party's primary were confined to paid-up dues-paying members of a political party, the candidates chosen wouldn't be as representative of the constituency as a whole and would be likely to lose the general election.