Each of those satellites in view would have to be implementing this scheme you suggest in order for it to be effective.

Since the satellites only have a single transmitter for each signal their entire receiving area would be affected by whatever modifications are made to implement SA. This means that to turn SA on for a single area more than half the globe would be getting a degraded signal from 1 or more satellites, which ones being undetectable.

I'm afraid SA is an all-or-nothing idea. Area denial (jamming) by surface and airborne transmitters is a much more workable approach. One could imagine jamming from space, but not using the GPS satellite vehicles.

So, to GPS. In the original GPS SA it is certainly true that many satellites would have to be using degraded mode to guarantee degradation for a specific point. However, the newer satellites have an additional directional antenna. While primarily for transmitting M-code to a specific region, it could equally be used for transmitting a self-jamming signal.