[DonRotolo]

The SRBs are compact, simple in operation and stable in handling.

Liquid boosters need complex engines and support systems (pumps, storage bottles, valves, etc.) and have to be filled with relatively volatile stuff shortly before launch. While you can get more thrust from a liquid booster, it is physically larger.

So the advantages of a SRB include reliability and simplicity of use. Disadvantage as you mentioned is lack of throttle control.

There are proposals to switch to liquid boosters, but highly doubtful this generation of shuttles will ever consider them.

Don