As much as I love the guy, the 1st person I ever heard refer to Rossi as the GOAT was Colin Edwards, sometime in late 2004 and if memory serves me correctly he did again during an interview for Mark Neale's 2005 documentary, "The Doctor, the Tornado & the Kentucky Kid", about the return to Laguna Seca.
From there, the Yellow legion & commentators ran with it, to the point that Keith Huewen on BT Sport can hardly refer to Rossi without calling him 'The Goat'. Keith is also the same numpty who can't refer to Luca Marini without calling him 'Luca MarinihalfbrothertoValentinoRossi'.
As to who is the GOAT? We'll never know, it's all subjective, what do you base it on, wins, longevity, danger, survival, personality? Through every generation there will be a best of that generation, but this Goat thing, Colin Edwards carries the can for us being stuck with it now.
My personal Goat will always be Mick Doohan based on what he achieved after that 1992 crash & the long road back.
All this talk of personalities & mental toughness is kind of laughable, we have no way of knowing if the persona we see on TV is 'real'. Most of the riders from the 'Golden Era' would be slammed on social media if they were still around today. They were motorcycle racers, personality didn't count. Doohan often accused of being cold or standoffish later admitted it was his way to deal with being painfully shy.
Back in 2012 in Aragon, I was lucky enough to meet Cal & Dek Crutchlow in the Paddock. My Mrs & I asked them for a picture and they went out of their way to be ultra nice to us, brought us into the garage to have the pics taken with the bike and chatted anytime we met them over the weekend. A complete antithesis of the personality Cal portrays in front of the cameras. We'll never 'really' know these guys.
Casey Stoner is weak? Spend every weekend at work being bitched at by Rossi fans, booed on the podium in Donington Park and spat on in the paddock (Casey reported this himself) for simply doing what you're paid to do, beat everyone else. Perhaps you or I would also want out of a situation like that. That's not weakness.
Casey was an enigma, I'd call him THE Enigma. Take Casey of 2006 to 2012, stick him back in 1990 and he'd have been the perfect rider in the perfect genre.
If we're going to over analyse these guys based on their personalities, it's worth considering all the factors, little schooling (or lack thereof), non-conventional upbringing, surrounded by their people through their formative years. These guys haven't had the normal personality developments that most of us in the real world are afforded.
If Marc Marquez was to bathe is the juice of freshly squeezed cats while inserting Liqourice allsorts up his chuff singing "I hate you all!", I'd still pay to watch him monster that beast on track.
Greatest of all time? There's no such thing.