The SRB thing isn't true. The costs ended up being pretty much the same for new vs. refurbed. The thing is, with solid boosters the "rocket engine" tends to just be giant aluminum cylinders, almost all the complexity of the job is in casting the fuel and putting the segments together, which is completely orthogonal to the reusability aspects.
Also, part of the allure of SRBs is that they are cheap to manufacture, comparatively (this is a false savings, due to increased operational complexity, but it's still very tempting), so even if a significant amount of money could be saved per SRB through reuse it wouldn't have affected the cost a launch much.
The SRBs don't just impose higher operational complexity, but also far higher acoustic load that requires much higher structural strength and therefore weight on everything else.
They also complicate the range safety situation and make on-pad aborts after they've been lit impossible. Once they've been lit you're going wherever they're going, whether you like it or not.
Pretty much, yes. They want to keep the people making those engines employed. I think there might be some talk about eventually going to a renewed F-1 engine with a much reduced complexity and greater thrust than the original. There is a reason why the SLS is also known as the Senate Launch System.
Also, part of the allure of SRBs is that they are cheap to manufacture, comparatively (this is a false savings, due to increased operational complexity, but it's still very tempting), so even if a significant amount of money could be saved per SRB through reuse it wouldn't have affected the cost a launch much.