In addition to what the previous answers are already saying, I would like to point out that recent developments have almost all been solid, even on the Russian and Chinese side. If you look at the DF-31, the Topol-M or Yars, you will see why military leaders like them: They are doomsday devices in the truest sense of the word. They can be deployed anywhere, even through rough terrain, kept there for years, and then fired within 10 minutes at the push of a button.
Not only is the propellant no immediate danger to the surroundings, they also don't need elaborate tubing to route the propellants, that eliminates problems that are known for hydrazine-based solutions, like the tendency of gasket materials to soak up hydrazine (or derivatives) and thereby gain volume and lose tensile strength. This could cause a rocket to suddently start leaking deadly propellant after quietly sitting somewhere for years.
As for synergy, I would say you're right on the money. France has long fought to replace the main engine of the Ariane 6 Launch vehicle with a solid rocket motor. This was in hopes that they could cut one of the two engine development programs that they finance. You see, for much the same reasons as the ICBMs discussed above France needs the solid fuels for it's SLBM arsenal.
For first stages this kind of makes sense. The specific impulse problem that jxexk talked about mostly rears its head in the final stage of a rocket. In the lower stages generating a lot of thrust is key, and solids are good at that.
However, they are expensive to make, and satellite providers are nervous about the additional vibrations that they introduce harming their precious devices.