Goodness knows, when it's not hard to do. I can think of a few... the best way is to target the neck as that will be guaranteed to be very quick.
A bullet in the back of the neck would do it, but no doubt the USA doesn't want to use the same method as China. Hanging will do the job if it's done properly, but the USA has a record of being incapable of doing it right so the country collectively doesn't like it. (What you need is to calculate the right length of drop according to the prisoner's weight, and that will cause death from a broken neck.)
And when vets can reliably give dogs a lethal injection, it shouldn't be beyond the wit of man to be able to do the same to people, but no...
a) states insist on messing around with mixtures of drugs when just one will work
b) many murderers are injecting drug abusers so the technicians struggle to find a vein to inject into
c) the medical profession won't have anything to do with killing people so "execution technicians" do it and they often make mistakes, like inserting the catheter into a muscle instead of a vein, which as anyone who's had an intramuscular injection knows HURTS.
Pain-free methods ARE available but the USA just won't choose them.