The solids were not a fundamental problem.
Challenger blew because the joint was designed to always be in compression--but it went into tension during the twang. After the headlines they paid attention and fixed it.
Congress insisted on the boosters to be made in other districts distant from the launch sites, so they were forced to make them in segments instead of a single continuous tube welded together permanently.
The risky thing about solids is that you cannot abort them. Once they light, there is no turning them off.
Shuttle always started the main engines for a few seconds (wasting fuel) to make sure the engines worked before lighting the solids. But there were many engine-out scenarios after the solids were lit that would result in loss-of-crew.