Solids are very precise, because they're used in a control loop with feedback. Liquids are somewhat more precise, but only somewhat. You can gimbal the thrust of both, and you can measure the thrust of both, and you can terminate the thrust of both. You only need the throttle control if you can't predetermine how much thrust you'll need, which is not the case during a launch, otherwise we'd have never launched a single Space Shuttle mission.
Keep in mind that you're arguing that small solids are useless for a 20 second imprecise launch application while advocating that we build entire launch systems to rely on them for precision performance, such as the Shuttle, SLS, and Delta IV.
This just shows you do not know what you are talking. Solids are open loop, there is no feedback. The thrust is not terminated in the solids used by the shuttle, Delta IV, Atlas V or SLS. They go until they burn out. Nor is the thrust measured and used in the guidance.
The solids have burn profile that can and does have variations from flight to flight. The shuttle flew an open loop profile during SRB burn and then went to close loop after to correct for dispersions. The same applies for the other vehicles.