That would be a SAFETY violation of the first order. You want to get to orbit.
Hence that was NEVER the primary "problem" of the Solids. The throttling issue has primarily been a shuttle-specific issue because it's "assemblage" is so fragile transiting throught the turbulence of supersonic+ speeds. Maximum vehicle stress needs to be ameliorated, hence they throttle back the SSME's which they can do...albeit it is risky since they are the primary means of vectoring (guiding) and stabilizing the whole assembly.
The problem of dynamic loads on the vehicle should simply vanish as a practical matter with the CEV design which hearkens back to the traditional Apollo configuration. The Apollo had a blast and dynamic load shield which protected the thin-walled capsule from such...which was jettisoned along with the Escape Tower when a critical altitude was reached.
"The LAST THING you want to do with your primary thrust is to SHUT IT DOWN.
That would be a SAFETY violation of the first order. You want to get to orbit"
Tell it to the Challenger crew.