So they didn’t have probable cause

Grounds for a traffic stop is RAS, not probable cause. It's a lower standard. Regardless, the officer clearly met both standards, because (according to him) he literally saw the driver not wearing his seat belt. That's the grounds for the stop.

he politely asked to speak to a supervisors

Which was completely fine. Not handing over his license was not.

This kind of shifting the reason for why something bad happened, from what you actually did that caused the bad thing to some other totally different behavior, is a classic tactic of people getting arrested and narcissistic family members the world over. Anyway, he got arrested for failing to provide ID (and then refusing to get out of the car), both of which he's required to do on a traffic stop. Asking for the supervisor was fine, it was unrelated to anything.

Also, as a side note, the supervisor will pretty much never override the cop in circumstances like this. All you're asking for is for another person (often with less patience and more authority) to come there and then assist the other cops with whatever they're planning to do with you. It shows a total lack of understanding of how anything works to demand a supervisor thinking that somehow once they arrive, your situation is going to get any better.

He just didn’t comply with what seems like an illegal order.

You can't argue on the side of the road why the cop shouldn't have pulled you over. If that were the system, no one in the history of the world would ever get a traffic ticket, because they would just say "I don't agree with the reason for the stop, so no you can't have my ID" and everything would grind to a halt until the cop's shift ended and the person got to drive away.

The system is, the cop can write you a ticket, and if it's bullshit, you get to go to court and fight it (in a calmer environment with an unbiased judge in charge of the proceedings and with you having plenty of time to prepare and even get a professional to help you argue it, if you want.)

Honestly, I'm just going to stop there. You guys just have no idea what you're talking about, you just see "Cop man bad!" and that's as far as it goes, and every other bit of fact and logic has to bend its way around that central axiom. IDK man. Good luck. I hope you do not get pulled over and try this, it would not go well for you if you did.