WGT can have their own version of the Open Championship if they want, however what made both the US and British nice for the WGT community was that they supported the WGT version. We got hats, USGA membership, etc. from these organizations in the past.
Today we get credits for qualifying, making it not seem as valuable or that you are a part of the real tournament.
I'm not sure what changed and why in terms of the US Open. I do know that after RSG there was an issue with the course that was hosting the British and an agreement could not be reached with WGT and since then it seems that no agreement exists between the R&A and WGT.
I would personally like to see WGT try to get a tie in with the PGA and have both the US Open and the PGA every year adding those courses.