It's not that clear cut. Both solid and liquid engines are problematic -- just different problems.

Liquid engines can be shut down, but this can cause spurious shutdown. The ability to shut down can't always be used, as evidenced by the Saturn V first 15 sec of flight. It takes more liquid engines to produce the same thrust, which drives up failure probability. E.g, if a Saturn V F-1 engine had 98% reliability, the total reliability for all five engines was about 90% -- and you must have all five working for some regimes. Those aren't actual numbers, but it illustrates that overall reliability goes down quickly with multiple engines.

Liquid engine throttling produces additional complexity and failure modes. There are various shuttle abort scenarios caused by throttle failures. We tend to think about previous failures, and evaluate risk on that basis. However if a shuttle or crew is lost due to a stuck throttle, that would quickly change.

Man-rated solid engines aren't simply manufactured and "hope for the best" -- they are X-rayed and tested hundreds of times. The shuttle SRBs are designed and built with a 200% structural margin, vs the normal practice of 140% or 150% for airframe and liquid engines.

Liquid engines require highly stressed turbomachinery which can have an uncontained failure and destroy the vehicle. Even with shutdown, that remains a risk. E.g, each shuttle fuel turbopump rotates at 30,000 rpm, and produces 76,000 shaft horsepower -- in the volume of a trash can.

It's true that solid rockets simply must work. However the same is true for various aspects of liquid engines. E.g, the shuttle propellent lines from the ET to orbiter require complex pyrotechnics and disconnect couplers. If they malfunction (fail to separate, separate but umbilical doors don't close, etc) -- the vehicle is lost.