Well those chems don't come cheap. Also there are also moral issues behind it. People don't want the guards to inject the prisoners and doctors take an oath to do no harm.
Also people think everything is cruel an unusual.
We use to hang people -> cruel and unusual
electric chair -> cruel and unusual
gas chamber -> cruel and unusual
firing squad -> cruel and unusual
The man/woman is going to get killed in the process anyway, you are better off just trying to directly get rid of the death penalty than
just doing indirectly because people are just going to look for new ways to legally execute people. Second issue is that you can't force people to change. If someone is going to change, then they are going to make that decision. You can offer as many chances to them, give them a free education, but when they get out they will probably go back to doing the things that got them there because that is all they know or society doesn't want them. The other issue is clothing, feeding, and housing an overcrowded prison population. One prisoner might be cheap, but then they start to add up.