I think I read the solid rockets are almost the same design used in the Shuttle, just a little bigger.
There's other problems it solves as well, safety being the biggest one. You don't have so many things to break, the capsule is on top of the rocket out of the way of anything, debris hitting the shuttle seems to be the biggest concern now. Probably the biggest safety gain they provide an escape mechanism not possible on the shuttle. That's what the little pointy thing is on top of the rocket.
The last rocket in that image is for payload only which is why it doesn't have it. The pointy thing is a small rocket, basically acts like ejector seat.