Peter
We studied the SR-71 installation back in my college days (~40 years ago). As noted, most of the 'thrust' comes from the inlet and exhaust, not the engine itself (at least at cruise Mach).
On the SR-71, the engine is there mainly to initiate the airflow through the ducts and to get the airplane up to speed. At ~Mach 3, ram jets are quite efficient, the problem being getting the aircraft going ~ Mach 2 so that the ram jet will actually work.
At cruise Mach numbers, the engine itself is of minimal benefit, except to provide hydraulics and electrical power. If not for the need for electrical and hydraulic power, and the weight of the associated hardware, it would probably be better for net thrust fuel efficiency to simply close off the inlet to the J58, let all the airflow go around, and make it a pure ramjet.
Of course, there would also be the concern of getting at least one of the jet engines running again at the end cruise (not trivial, after a prolonged high altitude cold soak
) for landing....
