Actually it doesn’t really matter all that much. If the Primary is closed many of the Democrats, already knowing who their own Candidate will be, temporarily change their registrations and vote in the Republican primaries instead of the Democrat primaries. They choose the Republican candidate or rather they reinforce the RNC’s choice. This time around there will be much more attention paid to the Congressional candidates, also.
Making people actually physically show up at the courthouse to register to vote or to change their party affiliation would stop a lot of those shenanigans.