Though borderline possible, it is very hard for solid fuel rockets to make it to orbit, and they have horrible payload to total mass ratios. It all has to do with the specific impulse of the fuels, no solid fuel provides as much as hydrogen/oxygen.
It's not so much just the Isp -- rockets can easily get to orbit on LOX/RP-1; LOX-LH2 is not needed -- but also dry mass of the stage. Basically the entire solid rocket motor is a thrust chamber, and must be strong enough to withstand that pressure. In a pump fed liquid propellant rocket, this is not the case: the tanks need only withstand a pressure high enough to avoid cavitation in the pumps.
Though borderline possible, it is very hard for solid fuel rockets to make it to orbit, and they have horrible payload to total mass ratios. It all has to do with the specific impulse of the fuels, no solid fuel provides as much as hydrogen/oxygen.