I've always wondered how a good boxer with no other kinds of training would fair in the octagon
Sh!tty, honestly. The very first UFC fights were like that - everyone brought a 100% pure style. The boxer was one of the worst. As soon as he got taken down, he was helpless. Fighters very quickly learned to blend styles. Everyone needs at least one striking art and one grappling art.
As an mma fighter, striking ability, which includes punches and kicks, is the skill set that sells tickets. Even fighters who are grapplers will be pressured to stand and trade punches, because that is what the crowd wants to see. Even if you win your fight, if you're boring, the promoter is not going to invite you back to fight again.
I think a pure boxing match plays right into Mayweather's hands. He is the world's best at manipulating the rules of boxing into his favor. If we wanted a fair fight, I think kickboxing would be a perfect compromise, say K1 rules. I would pay to see Mayweather get kicked around a ring. I think it would be hilarious. He wouldn't be able to get close enough to hug and stall. Or, we could go with Muay Thai rules, where he can hug all he wants, but gets to take knee strikes while doing so.