You answered your own question - almost. The class is the same, but the grandfathered status is not. Almost all of San Francisco's major FM's were built before Sutro tower, and before the FCC limited FM power to 50,000 watts at 500 feet or equivalent. Sutro is something like 1200 feet above average terrain, so power has to cut back significantly at that height. If you move a grandfathered high-power transmitter your new coverage area can not exceed your previous coverage in any direction. Most of the established high-power stations are on Mt. Beacon above Sausalito or on San Bruno Mtn. San Bruno stations get pretty good coverage down to San Jose, and there are some pretty high-powered stations there - led by KQED with 115,000 watts. If they moved North to Sutro the power levels go down fast, and they would lose that San Jose signal.
Similarly, a move from Mt. Beacon to Sutro also means a decrease in power. I can't find documentation for sure on this, but I heard that's what happened many years ago to 98.9. They have only 6000 watts or something like that because they lost most of their grandfathered status. The compromised signals combined with the cost of building a new transmitter plant and (I imagine) the high cost of site rent on Sutro probably makes it impractical for stations to move there.
Dave B.