Why? It's mainly so people of that party are the ones choosing the candidates for that party. Without closed the other side purposely tries to sabotage the otherside by voting for the worst candidate.
For example in the State of Oregon there are ~1M non party registrations. ~900k Dems, ~700k Republicans. Oregon is a closed primary state, thus the greater majority is not represented in the primary. https://sos.oregon.gov/elections/Pages/electionsstatistics.a...
How many of those non party voters even care enough to vote in a primary. My guess is very few and if they did then they should switch their non to a party.
My experience with primaries is only the most dedicated vote in them. For example in Nevada you have to sit in rooms in schools and listen to every nut that wants to give a ten minute speech to change your vote.