Izzy would be nowhere near being the GOAT of anything but maybe MW(one of those divisions where no one clearly deserves it IMO). Izzy became champ when the division was old/awful and he hasn't shown much in his first 4 title fights and adding more defenses won't prove anything because there's no one left in the division. Izzy is a 6 foot 4 guy at MW. It's the same criticism Jones got. 2 differences are Jones was at LHW and that Jones had the most dominant early run in history.
Let's look at Izzy's title fights. In the first one Izzy almost got KO'd in the fifth by a fighter half a foot shorter who had cardio issues. Whitakers his biggest win he's all that's left of the MW golden age but he might be a shell after those Romero wars(I also thought he wasn't the best of that era and his win streak was inflated). The Romero win is in theory great if they'd actually fought and Izzy's caution against Romero doesn't exactly inspire confidence. And Costa his other win was unbeaten but again he was unbeaten against a horrible division. Before winning a decision with Romero that could have went either way, Costa was fighting Hendricks and Uriah Hall. Finally if he's champ champ he'll have achieved it against the worst UFC champ of the modern era. There's 10 guys at LHW and HW each who could easily beat Jan. If he moves to LHW cause MW's empty and fights some of these guys who'd even pose problems for Jones then maybe now we're talking. But if there's one thing about champ champs we know they usually don't want to defend.
Champ champ IMO should arguably be a minus in the goat conversation cause trying to trick people into thinking you're a legend suggesting you couldn't do it the regular way. Izzy could clearly rack up defenses but that's cause MW is empty not cause he's an all time great. There's legit health reasons to switch divisions and wanting a challenge but this hasn't been what has happened. People say "I wanna switch divisions for a challenge" but the guys they've moved to fight suggests otherwise. Champ champ fights should only matter when you're going up to fight a legend and prove you're better(GSP v AS example). ZERO male super fights meet this criteria and even if you argue DC v Stipe does, Stipe was still easier fight for DC over Jones.
In the MW GOAT conversation though it is worth noting AS basically pulled the same exact shit as Izzy with Forrest minus the belt. Even fought irrelevant LHW's like Irvin and Bonnar cause some people would give him more credit for beating lower ranked LHW's than MW's(he did sacrifice defenses to do this though). . Was also taking advantage of his size advantage. I think no one deserves MW GOAT to be honest but no way Izzy's going to have as easy a time taking that title from AS as Marty is from GSP.