I am curious to why SpaceX wouldn't use more efficient solid rocket boosters instead of the liquid booster they currently have for the first stage of their Starships. At first, I thought this was due to the fact that catching the superheavy booster requires careful tunning of the thrust as demonstrated by their Ship 30 flight video. This seemed impossible with solid fuel, as it would have to burn all the way through and could not allow for such fine tuned adjustments. However, from analyzing the flight trajectory below, I do not see why the solid fuel couldn't be separated into two compartments:
The first compartment of the main stage would bring the Starship up into an ascent at a high delta V. It would then end the burn after Hot Staging, the flip back maneuver, and the boost back burn. Then, the booster would fall through the atmosphere, naturally deaccelerate, and then it could stop its velocity with a small second compartment through a retrograde burn. I understand that the timing would be extremely hard to pull off, but I feel like this could be feasible in the future, either in this form or some other system.