That's the trick to asphyxiation. It's not a lack of oxygen that hurts. It's a buildup of CO2 in your blood. But if there are other gases in your lungs, nitrogen for instance, the CO2 can filter out via partial pressure gas exchange, and you won't notice you aren't breathing oxygen. It feels like nothing and then you die.

Off topic tangent: It's actually the most humane method of execution/euthanasia. The only reason we don't use it for everything is because it's dangerous to everyone else too. If there's a nitrogen leak, you might never know. There are multiple cases of someone coming across bodies lying on the floor of a laboratory. The person who finds them runs in to rescue them and never realizes they're running into a death trap. They die too.

That's why we should use helium for execution instead. All the benefits you've mentioned, plus it rises and won't pool on the floor, and people's voices would sound hilarious.