Not in the slightest.
The protocols for euthanizing small animals are written by doctors and veterinarians and scientists. None of those people want anything to do with executions, so the protocols for executions are generally written by people with little medical training, and the people conducting the execution are in a similar boat.
The result is that execution protocols are far from optimal. Take for example the typical three drug cocktail- first drug knocks you out, second drug paralyzes you, third drug stops the heart. Only problem is the third drug is extremely painful so if the dosage of the first drug is too low you can be conscious for it but unable to move leading to one of the most torturous painful deaths you can imagine, which nobody on the outside has any idea is going on because you are unable to move.
A much better execution protocol would be something like fentanyl or a single massive overdose of barbiturates. Either one you would just pass out and die quickly. Another option is nitrogen, the air we breathe is 80% nitrogen so the body doesn't react to it. Simply give somebody 100% nitrogen 0% oxygen, the brain is starved of oxygen, you get painless euphoric unconsciousness in under a minute and death in under 10 minutes. It's also cheap as hell because it's all around us.
Thing is- speaking for myself, as a pilot and scuba diver I understand exactly how nitrogen hypoxia works and I could write a 100% bulletproof execution protocol that could be administered by a trained monkey and would lead to a rapid painless death every time. I won't do it. You could pay me a million dollars and I wouldn't do it. I don't have faith in our criminal justice system prudence to execute people. There are too many situations where innocent people have been convicted and executed and the system did not properly consider the evidence in their favor. As such I don't think it's ethical for me to help a system kill people when I don't have faith that they are always going to kill the right people and not the wrong ones.
And the thing is, and not the only one. There's an awful lot of doctors and medical technicians in this country, and prison systems still have trouble finding ones to deal with executions. There's tons of pharmaceutical suppliers in the world and prison systems have trouble finding ones that will supply execution drugs at any price. The vast majority of people simply do not want to be part of capital punishment.
And as for who pays, it's the taxpayer. Given the actual execution and all of the legal hurdles involved, it is a good bit cheaper to just incarcerate somebody for life. Which makes you wonder why some people are so dead set on having a death penalty when for less money we can just lock them up and throw away the key.