Phil,
I am assuming on a daily basis that the plus player plays the tips, the scratch player plays the typical back tees and the bogey player plays the member tees.
I don't know Bethpage Black well enough to comment on how difficult it is for a wide range of players. I was playing between scratch and bogey that day and I didn't find the golf course overpowering. I was used to uphill approaches though as a onetime member of Rolling Green GC.
As for Shinnecock Hills, on a daily basis, the golf course is a great example of enjoyable difficulty for all classes of players from plus handicappers to grandmothers. There aren't any overly long carries and the wispy fescue makes for reasonably difficult recoveries. However, the golf course is not kept very firm so that it plays quite a bit easier than as setup for an Open. It will be interesting to see how much of the newly recovered green space (ongoing project) is used on a daily basis. Don't get me wrong, Shinnecock Hills can be set up very hard for any class of player. It isn't on a day in and day out basis though the amount of wind has a significant impact as to how difficult the course plays.
It may surprise many, but Merion East, even at 6480 yards, is a very difficult golf course on a daily basis for plus and scratch players. The physical and mental demands of the course are extremely difficult, especially compared to preconceived notions based on the scorecard distances. I can only imagine how difficult the course plays on a daily basis from the championship tees, just under 7000 yards. The physical demands of the course require accuracy off the tee and on approach shots. The firm and fast conditions through the green and on the greens themselves require excellence in ball striking, distance control, correct shot shapes considering the landing area topography and the correct game plan. The thickness, not length of the rough (it is only about 2.5-3 inches) tests the patience and control of the player. Finally, the fast and hard to read greens have a variety of sizes and slopes that dictate ideal approach angles influencing the tee shots and all subsequent shots.