Yes, the US Constitution gives regulation of interstate commerce to the federal government, but this has been worked around. Lots of states have "use tax" which is an obvious[1] tax on interstate commerce, but they skirt the Constitution by saying they're taxing "use" of the goods purchased within their own state, not the interstate commerce involved. It's possible the AZ law could be written in a way that claims to tax something that happens within the state, while still being for all intents and purposes a tax on interstate commerce. And probably nobody would do anything about it.
[1] The tax is computed 100% based on the money exchanged in interstate commerce, and 0% based on usage.