Why don't they use nitrogen in US executions?

Two reasons.

1. Many states have laws that specifically require an "injection".

2. Use of any gas to kill is slightly too similar to what the Nazis did for some Americans to be comfortable with the idea. (The Nazis didn't actually use nitrogen; the problem is essentially that the phrase "gas chamber" is too closely associated with them.)

It is not a 100% sure thing.

Or better still, move into the decent world of not murdering people

It doesn't "replace" oxygen, because nitrogen does not bond with hemoglobin. It just isn't oxygen. The body senses a buildup of carbon dioxide, but not low oxygen (at least, not very fast). As long as you're breathing out N2 + CO2, the body thinks it's getting rid of CO2 as per usual. Argon, neon, helium or any other inert gas would have the same effect. But doncha think prisoners would hold their breaths as long as possible, thereby experiencing "cruel and unusual" suffocation? For the same effect you could tape their mouths shut and hold their noses, make them breathe carbon monoxide, drown them, hang them by the neck until dead, or see how long they last in a vacuum. It's all lack of oxygen, dude.

Because politicians haven't heard of it yet. And if they had any sense, they'd abolish the death penalty altogether.

or they could use potassium chloride , readily available as a salt substitute in any supermarket