I think the USGA already has a very unofficial and fluid U.S. Open rota.
They currently want to hold periodic Opens at Shinnecock, Winged Foot, Bethpage Black, Oakmont, Pinehurst #2, Pebble Beach, and Olympic.
Next they have some interest in possibly revisiting Oakland Hills, Oak Hill, Southern Hills, Baltusrol, Congressional, Hazeltine, and possibly very occasional visits to Merion & The Country Club.
Finally, they can not figure out what to do about getting an Open to Chicago or at least the greater Chicago area, and possibly elsewhere in the Mid-West. They are also open to exploring other locations on the West coast.
A variety of issues will cause fluctuation among this rota. These may include the course hosting the PGA or other tournament, the current membership not wanting the open, logistics complications, revenue limitations, etc. But, although one of the above courses may fall out of the active rota, they may still remain as future possible hosts once the issues can be worked through. However, it does appear that Inverness and Cherry Hills have likely dropped out of US Open consideration.
In addition, it appears the USGA has no interest in being in the South other than Pinehurst #2. Southern Hills to Congressional would appear to be as far south as they want to take the Open (east of the Rockies) other than Pinehurst.
Any location outside of these parameters will be very rare. Only 7 courses have hosted the US Open since post-WWII that are not among the 17 courses named above and that are outside of Chicago. Interestingly there will be two visits to courses during the upcoming decade outside of these parameters (Chambers Bay & Erin Hills).
So over a 74 year period (1946-2019) only 9 courses will host the US Open other than the 17 courses listed above and outside of Chicago. That is a rota is about 13-17 courses, + a Chicago course, + 1 or 2 others per decade.