In June 1986, the Soviets were finally able to mount a successful SR-71 intercept using their new MiG-31 Foxhounds. In a coordinated intercept over the Barents Sea, six Mig-31s subjected a lone SR-71 to an all-angle air-to-air missile intercept. Fortunately for the American crew, they were over international waters, but the Soviets had proven their point. I’m guessing that once the Blackbird lost its aura of invincibility, the Air Force decided to phase it out and look for something hypersonic rather than supersonic.
Not sure how the MiG-31s would get in position to intercept a SR-71. The Blackbird cruised at M 3.2 at 80,000+ feet. The MiG-31’s top speed is M 2.8.
It’s a simple matter of geometry.
The only way this would have been feasible is if the MiG-31s fired long-range AAMs similar to the USN Phoenix. But there is no way to have been sure of such a shot without actually firing the missiles and seeing the actual results.