Maybe you should push that for the prison system, sounds much cheaper and efficient than most forms of capital punishment they use these days.
I'll ignore the tangent that this post sparked, and say that yes, it should be the approach.
But humans are not always intelligent, and view "suffocation" as inhumane.
Some animal shelters employ Nitrogen or Argon, and some communities then seek to bar the practice, in favor of chemically-induced euthanasia as opposed to the horror that is painless asphyxiation.
Sadly, part of the issue is many gas chambers still employ carbon monoxide, which, while technically painless, if concentrations are wrong, it may not prompt loss of consciousness and thus instead promotes confusion and aggression in animals.
But the right approach is choosing an inert gas.
Gas chambers used to be lawful for lethal executions, though they almost always used toxic gasses, which is mostly why it fell out of favor, as effects could be prolonged.
It's too easy to demonstrate that inert gasses cause painless asphyxiation, as one can immediately return oxygen to the victim and recount the experience.
Asphyxiation is only painful when carbon dioxide is not allowed to escape the body, as in increased dosages beyond what our body produces naturally, it is a toxin, and causes immense pain. If you can inhale and exhale, you complete void your lungs and blood of carbon dioxide and remaining oxygen, and fail to introduce any new oxygen. It wouldn't be like holding your breath, as in unassisted diving, because you are going to great lengths to preserve all unused oxygen. Complete oxygen deprivation but painless breathing would be confusing at first, as the lack of pain would encourage you to continue breathing, and it would only take 30-60 seconds to render the body unconscious. Possibly convulsions might cause onlookers some distress, like they freak out about those experienced while unconscious during lethal injection, but suffice it to say, induced death rarely appears peaceful unless you go for any of the instant brain-kill approaches.