Yes, it's preferable to have solid propellant missiles. But that does not mean it's impossible to use liquid, and even cryogenic liquid fueled rockets for deterrence missions. The first American ICBM, Atlas, used liquid oxygen, and was used for 7 years. Its contemporaneous soviet counterpart, the R-7 Semyorka, also used liquid oxygen and was in service for 9 years.

The advantage would be pre positioned orbital interceptors could effectively reach some percentage of missiles in the boost phase rather than later on when intercept is harder.

Starship also allows for enough mass to orbit to make Star Wars legitimately viable.

There could be a case made that Spaceship will fly so often to allow novels method to eliminate most problem related to that.