Although, I am puzzled why some PHA GLS requests no recognition.
More issues than just recognition. All sorts of details have happened.
MWPHGLofOK has local recognition but they have not requested recognition from UGLE. They don't say why. Many of us have guesses that have been mentioned in other threads, but anyone not present during their annual/quarterly Communications is just guessing. Not having UGLE recognition means that world wide, their members can't visit. As they sponsor lodges on military bases all over the word it's very puzzling to not want to visit.
MWPHGLofCA requested that no cross affiliation be included in their agreement. This strange feature has been included in every PHA recognition that GLofCA has offered ever since. MWPHGLofCA are (were?) a single affiliation jurisdiction so anyone petitioning for affiliation would be required to demit anyways. That means the request doesn't actually matter or make sense. We could guess there was a different intent than the actual wording but that's just guessing. I think the intent was to prevent PHA members from transferring but that's not what the agreement said.
Either MWPHGLofAL or GLofAL requested that no visitation happen for 10 years. They also don't say why. As seen in this thread, guessing has an extremely high failure rate as we technically don't even know which side requested that feature. The 10 year timing isn't unique - Texas waited about that long before setting up visitation details.
Search around and I bet there will be other restrictions in one compact or another.
Just as an anecdote, I faced an unusual situation for a time. I am a member of both GLoCA and GLoKY. Both have recognition of PHA, but KY at that time did not allow visitation. It dawned on me that if I was sitting in my lodge in CA and a PHA Mason came to visit...what do I do?
Most jurisdictions have an "act like the locals" rule when visiting. As a member you aren't visiting but since you would be in a California lodge at the time, local would mean California. Visits between MWPHGLofCA and GLofCA are very common. My mother lodge has a PHA lodge as a tenant so we only have to walk to the next room. You would act like a local and welcome the visitor to your own lodge.