Of course, you cannot guarantee to intercept a target with a single plane, but that's hardly unique to the SR-71.
> The MIGs would have had to accelerate to Mach 3
Not really. In any realistic interception scenario, the 2.83 Mach safe maximum speed would be sufficient to intercept successfully. Going at Mach 3 or more would be most useful in case of emergency.
> could accelerate, climb, an|or change direction to evade the MIG.
We are assuming the SR-71 is already at maximum altitude and speed. Changing direction is a bad idea because the SR-71 turns very slowly at very high speeds, so it would have to slow down, which is counterproductive.
The MiGs were able to gain altitude around 4x as fast as the SR-71. They could get to the maximum altitude of the SR-71 and close to their maximum speed in around 10 minutes from the ground.
> the predecessor to the SR-71 did carry air to air missiles
The YF-12 never made it to initial service, it's production predecessor, the A-12, did not have armament. No version of the A-12 was ever made that could both do reconnaissance and carry weapons.
> Having intelligence as to from where and when the SR-71 was coming would probably be crucial.
Definitely. But again, you're just describing interceptions in general. Without having vectors and warning at least ten minutes (which means only 600km for the SR-71) in advance, you can't really intercept anything.
Of course, a single MiG-25 wouldn't have had the best of chances. But a pack of MiG-25s would definitely have very good chances. In actuality, SR-71s were indeed intercepted by MiG-25s in international airspace.