Lots of problems with firing squad and/or hanging. Most have to do with lawyers. Firing squad requires dealing with the cleanup and possibly contaminated (HIV) blood. Hanging gets into ripping heads off of fat people and not enough drop for slight people ... etc.
With the Nitrogen Asphyxiation, they go to sleep. Nothing for a lawyer to try and hang his hat on. No cruel and unusual, no blood, no “excessive” pain, always works, no drugs to expire, run out of , or manufacture to withdraw.
Well, there is no humane way to kill someone if all errors must be eliminated. But I’ve got no problem with your proposed solution.
You can bet some lawyers will, though, because what they really object to is the possibility of punishment.
Lots of problems with firing squad and/or hanging...
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Just send them to Planned Parenthood and tell them they missed one.