Death by firing squad is relatively humane (especially in comparison to electrocution), so if you really need to have capital punishment and your options are electrocution and firing squad, the choice is pretty clear. I think the reason executions moved away from firing squad was that it was mentally taxing of the people in the firing squad, not because the alternatives were more humane.
It really doesn't matter to the person being executed. I think changing it is more about the sensibilities of the observers.
If I were on death row I think I’d very strongly prefer a firing squad. If I were the person performing the execution… perhaps not.
But I think you’re right that these changes aren’t being brought about for the benefit for the executed. It’s embarrassing for those executing when one goes wrong and states have had to resort to more and more obscure cocktails of drugs as companies refuse to sell when they know their product is being used to kill. By comparison a firing squad has a very simple supply chain.