Because the electorate in open primaries more closely resembles the electorate in general elections, so the candidate who wins the open primary is more likely to win the general?
Plus, in those states that you mentioned open primaries -- until rather recently -- mean conservative Democrats voting in Republican primaries.
Arguably, there was a day when open primaries could have meant more conservative Republican nominees, rather than fewer.
Either there is a large conservative voting bloc outside registered GOP voters that will go with more conservative candidates in the primary and general election or there isn't.
If there is, then you'll get more conservative nominees and representatives. If there isn't, you won't. A closed primary won't change that.
“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?