Most states in the US that administer the death penalty, as well as the federal government, use lethal injection as their method of execution. In almost all of these jurisdictions, the method used is the successive administration of three drugs in specified doses. This particular legally prescribed procedure has been criticized for not having originally been based on careful science, for using outmoded drugs, and for possibly causing extreme suffering in some cases at the end of the condemned person's life. It would be trivial to develop better and more modern procedures that would be immune to this legal vulnerability, and, for instance, Missouri has attempted to do this by switching to the modern anaesthetic propofol. I'm not a doctor, but it seems obvious to me that this should be scientifically easy to do, since, e.g., opioid addicts die peacefully of overdoses all the time, and veterinarians don't seem to have any problems carrying out euthanasia on someone's beloved terrier in a painless way.
Why, then, is this battle still being fought? In states where the state government and the majority of voters favor the death penalty, it would seem to be in their interest to redo the protocols. They could then accomplish their goal, to carry out executions, without having to deal with legal challenges based on the theory that the method was cruel and unusual under the constitution. It would also seem to be politically expedient for them because it would eliminate one of the moral arguments used by their opponents. And there are some people who believe the death penalty is moral, but that it's immoral to do it in a way that causes unnecessary suffering. For these people, it would seem ethically necessary to support a change in the protocols.
Is the inertia because the poorer protocol has already survived legal challenges, while the new one would still have to? Is it because they're afraid that this would be seen as an admission that they'd been using a bad procedure in the past? Is it just not the kind of legislative project that appeals to lawmakers politically? Is it because they might have difficulties obtaining drugs like propofol from suppliers who don't want to sell them for this purpose? But it seems that there are severe difficulties in obtaining supplies of the currently prescribed drug cocktail as well.