I’m totally in favor of closed primaries, and you explained well why.
Let the parties pick our strongest candidates without interference. If you want to be independent or undecided, fine. But, wait until the general election to vote then.
It’s not like those who are independent or undecided or didn’t meet the party’s requirements in time would have no influence in the process. They are still free to volunteer their time, donate money, and engage in face to face or online discussions with other people (including many who are party members and will be voting in the party’s primary) as to why they support candidate X. And I suspect the sort of system I proposed would also promote the development of viable third parties — a positive development from the viewpoint of those of us who think competition is a good thing.