Why would you want to do that even with a liquid fueled booster?
The power is reduced after liftoff so the stack will encounter less drag and turbulence while in the atmosphere. Once past the point of maximum drag and turbulence, the engine thrust is increased.
For one, the thrust of a liquid-fueled engine is adjusted to limit aerodynamic and thrust loads on the launch vehicle / payload during flight. Recall the last transmission from Challenger was, "go for throttle up", when the craft had passed the region of maximum aerodynamic forces on the vehicle.
> Why would you want to do that [throttle or shut down a
> booster] even with a liquid fueled booster?
If an incipient major malfunction can be detected early
enough, the booster can be safed before it causes a total
loss of the stack.
Note that the proposed Crew stack has a small escape
rocket on the top of the capsule, as Mercury-thru-Apollo
did (never used, but the USSR had to once). This only
works reliably if what you are blasting away from isn't
still accelerating toward you (or exploding parts at you).
With a good escape system in place there should be no reason to throttle the SRB. If you need to shut it off in flight, the mission has already failed and you will be firing the escape system anyway.
It is significant that there has never been a catastrophic SRB failure on the STS. The o-ring defect that destroyed the Challenger was catastrophic only because of its effect on adjacent systems and would not present a significant risk to the proposed manned system.
IMHO, these systems look like a solid replacement for the shuttle. They are by no means ideal, but in the world of aerospace the better is always the enemy of the good.
The throttle the main engines on the current shuttle to 75% to conserve fuel. I guess that would be one good reason.