Medical professionals, particularly doctors who have sworn an oath against causing harm, refuse to take part in the executions. This is partly why lethal injections are so hit and miss. Even if you can get the drugs, the dosages are tricky. IV placement is a skill. All of it being done by untrained individuals leads to a high rate of failure- and that was before the pharmaceutical companies started refusing to supply prisons.

I would imagine that if benzos became part of the nitrogen hypoxia protocols prisons would then have a hard time sourcing them, which is terrible for those other inmates who might need them for other reasons (anxiety, alcohol withdrawal, seizures)