Roger Federer has time for everyone: opponents, fans, umpires, even the media – but nowhere in the world away from his mountain retreat does the mutual love and respect between the Swiss and his followers seem louder and more unconditional than in Melbourne.

As he savoured his sixth Australian Open on his way to a night of no doubt impeccably behaved celebration, he engaged with everyone who wanted to spend even a second in the glow of his royal progress. And, when it was suggested to him that Federation Square near Flinders Street station in the middle of the city be officially shortened to Fed Square in his honour, he blushed and smiled.

“Fed Square, eh? That’d be cool,” he said to the other part of his post-match double act, Jim Courier. “We’ll make it good. Rock it.”

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Only a couple of hours earlier, he had dragged himself through such an emotional wringer – beating Marin Cilic 6-2, 6-7 (5), 6-3, 3-6, 6-1 in just over three hours under the roof on Rod Laver Arena – that he broke down in tears at the end of the courtside presentation. Later, he revealed why. “My thoughts were all over the place all day. I was thinking, ‘What if I lost? What if I won?’ Like all day. By the time the match comes around, you’re a wreck.”

Who would have thought that the 36-year-old father of four with the perfect life and a bank of achievement in his sport that might never be equalled would be capable of such vulnerability? He has never shown us this side of him before – although he said later: “I have felt it many times.”

As for his performance, which swung between outrageous genius in the 24-minute first set, through a perplexing struggle mid-match and on to a devastating finish, he said: “I had my chances. I think I froze in the [second-set] tie-breaker. And I got nervous in the fourth set. I couldn’t stop the bleeding, almost. He was in control, calling the shots. My mind was all over the place in the fourth set, like, ‘Don’t mess it up.’ I had to get lucky at the beginning of the fifth set. And I could see he was feeling it.”

These are rare and candid insights into the mind of a champion, a player who has risen to the stratosphere of his sport, slipped and climbed again, looking back from time to time to check on his younger rivals, who have tumbled from view. No Rafael Nadal in the final this time, after last year’s epic comeback to rob the Spaniard of the glory; no Novak Djokovic, who is contemplating surgery on his elbow; and no Andy Murray, who has already taken that route to mend his hip.

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Federer has sailed serenely on, inhabiting a cloud that is eternally silver-lined. And he shows no sign of leaving the stage. It is 15 years since he appeared in the first of his 30 grand slam finals, when he beat Mark Philippoussis at Wimbledon. His first Australian triumph arrived the following year. Then came a string of wins that lit up the sporting universe like a blazing sun.

“Everything changes in your life after your first,” he said – as if ordinary people would understand what that was like. “This one reminds me of 2006 against Marcos Baghdatis. I was keeping my composure. And then I was so relieved. I felt the same way tonight. It was terrible.”

He meant terrible to endure but wonderful to revel in after his last serve was called good. And there to applaud with all the others was the man in whose honour the main stadium here was named, Rod Laver. Lining up his mobile phone, he snapped away from the stands to record the moment Federer raised the Norman Brookes trophy for the sixth – and probably not final – time.

Federer said: “He’s the best. The Rocket. I’m so happy when I see him. It’s because of the legends of this sport that I play tennis. But I didn’t even see that through the tears. I couldn’t lift my head. I was so embarrassed.”

Facebook Twitter Pinterest Roger Federer kisses the winner’s trophy after beating Croatia’s Marin Cilic. Photograph: William West/AFP/Getty Images

There is a view that Federer lacks self-awareness, that he sometimes says the most gauche, self-serving things when praise is heaped upon him – which is most of the time. But this almost boyish grinning also talks to the innocence still in him. He has won everything, been everywhere, done things with a tennis racket even his peers marvel at, and yet he plays on because he loves it.

The inbuilt addiction of hitting a fluffy ball with a racket is as incomprehensible to him, probably, but as strong as when he was a child prodigy. And, in the serious heat of battle on a night of fluctuating drama – when he might so easily have lost had he not regathered his composure in the fifth set – he drinks from the cup of innocence. He plays a grown-up game with the freedom of a child, and that is a rarity that defies proper description.

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As he wandered from one interview to another, passing the tournament staff and fans who did not want to go home, he never stopped smiling. “Thank you guys,” he shouted to them. “Thank you for your support.”

And that is the other secret to the Federer phenomenon. He feeds off the adoration. He probably cannot imagine what it is going to be like without it, or at least this very public version of it.

“We love you, Roger,” screamed one star-struck fan after another as he disappeared back into the bowels of the building to be grilled more formally by his friends in the media. This is his life.