You might, incidentally, want to read up on the “painless” part of inert gas.

I don't need to. I've experienced it. I've stuck my head in big reaction chambers before all the Argon has dispersed, and I know exactly what it feels like. If I were suicidal, that's how I'd do it, and in fact, that's how many people choose to go. It's here one second, light headed, then gone. We can detect the overabundance of CO2 in our lungs, but not the absence of O2, so there's no biological panic signal. Just nothing.

The US doesn't execute people this way because something something "cruel and unusual doesn't allow people to feel slightly high on the way out." It's bullshit. A humane society with the intention to euthanize or execute people would do so with N2 or another inert gas. We don't because we choose to be cruel.