Would you like to see a law that Presidential primary election occur after June 1st in the election year?

No.

Problem with that law is the federal law controlling campaign finance. Campaign finance law treats the primaries and the general election as two separate elections for the purpose of the cap on donations. As a result, the two parties have an incentive to hold their conventions as early as possible so that candidate can hit max donors for the second check.

A June 1st primary would force states to recalibrate how they pick delegates for the conventions. (Many of the states that go earlier choose delegates after the primary.) Additionally, if you are having a one-day primary, you are almost guaranteed to have a deadlocked convention because there will be five or six candidates on the ballot, each candidate doing well in a different state or region.