The Blanket primary was dumped based on lawsuits from the main political parties challenges.

Primary elections are held to determine which candidate from each party will run for any given office, not which individual will be elected to serve in that office.

Use the Dems Repubs and Libertarians as a example.
According to our old blanket primary, these organizations, once they announced their intentions, would not be allowed to pick their own candidate but would have to list several members on a public ballot so any voter could determine who get to run in the general elections.

With the new primary system political parties pick the candidate that best fits that party's goals.

If you are not a member of that party, you should have no say in which candidate they select is the theory.