Some have even thrown up Serena as a contender for one of the best athletes in history, given her dominance of the courts over nearly two decades.
But now, probably not a chance.
Williams (23 majors) has been a wonderful player, and may even capture two more grand slams before she retires, which would take her ahead of Margaret Court (24).
But for many tennis aficionados, she'll never be held in the same regard the likes of Steffi Graf (22) or Chris Evert (18).
There's much more to being a great than lifting the trophy, and Williams has now failed that test several times.
As for ranking her ahead of Roger Federer, Rafa Nadal or Rod Laver?
That would be a stretch.
All of those players were great statesman of the sport, generally respectful of the traditions, the fans, the game and their opponent.
Williams' behaviour in New York last Sunday was inexcusable.
It's understandable to lose your cool in the heat of the moment, but the fact she carried on way, way beyond the reasonable, then continued with a curious agenda in the press conference, wasn't becoming of a such a champion.
Williams appeared to do everything possible to deflect attention from Naomi Osaka's victory, despite the fact she was outplayed by the rising star.
It has continued a pattern of behaviour by Williams, especially in a losing situation.
Remember 2009 at the US Open?
Williams was down 4-6 4-5 15-30 against Kim Clijsters when the line judge Shino Tsurubuchi called a foot fault on her second serve.
It was an unusual call, but prompted an incredible reaction.
She stormed over to the line judge, and among other threats said "I'm going to take this ball and shove it down your [expletive] throat".
Williams refused to apologise after the match, saying she didn't think it was necessary.
In 2011, again in New York, Williams lost the plot after a hindrance call from the umpire in the final against Sam Stosur, when she was down a set and a break.
"Are you the one who screwed me over last time?," she asked Eva Asderaki, launching into a tirade. "If you ever see me walking down the hall, look the other way because you're out of control, you're out of control. You're a hater and you're just unattractive inside. You get a code violation because I express who I am. We're in America last I checked. Really, don't even look at me. I promise you don't look at me because I am not — don't look my way."
Last year in Auckland we got a small taste of the other side of Serena.
It was great that she even came to New Zealand – to play in such a boutique event – but her conduct after a shock second round defeat at the ASB Classic was regrettable.
In just her second - and final interview at the tournament - Williams spent most of the three minutes and thirty seconds attacking the credibility of the event.
That may not have been her intention, but when someone with the American's standing says that the blustery afternoon in Auckland was "the least favourite conditions I've ever played in" it felt like a dagger blow to its reputation.
Williams added that the ASB Classic "was not a great opportunity to assess your game", a comment that can reverberate around the locker room.
