Semi private is like semi pregnant. Really doesn’t exist. You are either private or you are public. Nothing in between.
I just... there are so many types of organizational structures that this dichotomy is silly at best. ANGC is a for-profit comany that chooses not to allow public access. Invited/ClubCorp is a for-profit that choses to allow public access. Most "private clubs" in America are 501c7's that can't advertise or offer tee times to the public, however, they are allowed to let you play if you inquire about playing, and many do. UK clubs don't have these restrictions so most offer tee times to the public, some don't, and some on rare occation. Many American clubs are equity memberships that allow public play, but don't have to. There are also essentially public clubs that offer memberships to get priority play times.
There are a half a dozen ways clubs can be somewhere in between fully public and fully private. Insisting it must be one or the other without substance is just a form of a no-true-scotsman argument.
You can’t have a dozen categories for rankings. That would be stupid. Either have only one category (Golf course) or two (private or public). With only two, then any course that allows any public non guest play is public. So, Lido is public. No big deal. Another example. Linville GC used to be public. I played there several times and was not a member. Guests at the Esseeloa lodge used to be able to book tee times. Not anymore. Therefore, Linville GC is now private and should be listed as one of the best private courses in the US. Lido should be listed as one of the best public course in the US. As it is. Seems pretty straightforward to me.
So what are Sunningdale and Royal Melbourne and Muirfield and Royal County Down, etc?
Sunningdale et al. are in a category all by themselves. They are very private for residents but are gracious to overseas players like me. The same holds true for some US courses that offer to host players that belong to the Sunnningdales of the world.