My $0.02...
East
Brookline
Winged Foot
Bethpage
Merion
Southeast
Pinehurst 2
South
Shoal Creek
Midwest
Oakmont
Chicago Golf
Camargo
Southwest (TBH I have not visited this region much)
Southern Hills
West
LACC
Riviera
Olympic
Pebble
Northwest
IDK
That's 15. Gives every significant player a chance to get thru the rotation once in his career. Also gives the clubs and communities a chance to work up an appetite for the huge commitment that hosting a modern major requires. If I was the USGA I'd require a couple of other caveats; the courses above must also host the Womens Open, and they must allow as least a token number of annual unaccompanied players similar to Muirfield or Troon.
I love what the USGA has done with the Walker Cup, hoping they continue murderer's row with SFGC, Somerset etc in the future.
An Open rotation would give the PGA a chance to define it's major as a showcase for new and different courses.
One final thought for the board - with the improvement in coverage technology, and the mega $'s from the TV contracts, is it possible the USGA will consider scaling back ticket sales in order to make a ChicagoG or Camargo a realistic option?
Never understood for the life of me anyway why 40k people would cram into a course on a Sunday with almost zero chance of having a decent view of the deciding shots. Go for a practice round to walk the course, camp out on a hole on Thursday or Friday to see all of the players, but watch on TV if you wanna follow the outcome on the weekend.
MW