Goncalo Ramos celebrates
Santos expressed his displeasure at gestures made by Ronaldo when he was substituted in the last group game against South Korea and it was the first time in 31 games stretching back to 2008 that he had not started in a major tournament.
Portugal made light of the 37-year-old's absence to put it mildly, as 21-year-old Benfica striker Ramos hit the first treble of this tournament on his first international start, to help set up a quarter-final against surprise package Morocco after their win against Spain on penalties.
Ramos started the rout after 17 minutes when he drilled a finish past Swiss keeper Jan Sommer at the near post before veteran 39-year-old defender Pepe doubled Portugal's lead when he headed home Bruno Fernandes' corner in the 33rd minute.
The dream full debut continued when Ramos effectively ended the contest with a near post swoop on Diogo Dalot's cross six minutes after the break, the striker turning provider to set up Raphael Guerriero to round off a sweeping move with a powerful strike four minutes later.
Manchester City defender Manuel Akanji pulled one back for Switzerland but Ramos swiftly got his third with a clever chip, which was the signal for the crowd at Lusail Stadium to noisily demand Ronaldo's introduction.
Portugal coach Ramos obliged with the game won, Ronaldo entering to rapturous applause, but his team-mates deserve all the acclaim for a high-class performance.
Ronaldo had the ball in the net but was ruled offside so it was another young pretender to his crown, 23-year-old Rafael Leao, who crowned a dazzling display when he curled in the sixth.
Cristiano Ronaldo's absence did not remove the spotlight and attention from the fading superstar but actually made it shine even more brightly in his direction at Lusail Stadium.
Ronaldo was swarmed by photographers in the dug-out after the national anthems then received a pop star's welcome when he came on as substitute after 74 minutes following prolonged and noisy demands for his introduction, particularly from the locals who had come to see him in the flesh.
The focus should not be Ronaldo though.
The credit must go to a Portugal team who looked more mobile, fluid and unified without the man who is currently searching for his next club having left Manchester United.
Portugal is a team full of talent even without Ronaldo and Ramos made an instant impact, not just with his goals but also his movement and team play.
And the sweet late strike from Rafael Leao was another demonstration of Portugal's bright future, one that hardly looked in jeopardy without Ronaldo as they swept Switzerland aside.
Portugal coach Santos is a stern-faced individual but a shrewd operator with a Euro 2016 triumph on his CV. He would be fully justified in allowing himself a smile after his brave, but ultimately correct decision, to leave out his team's towering presence.
This was such a complete performance from Portugal that there is surely no starting place for Ronaldo in the upcoming World Cup quarter-final against Morocco.
Switzerland made their way into the World Cup last 16 with a reputation as a stubborn, well-organised and hard to beat team under the direction of experienced coach Murat Yakin.
If so, this was a pale imitation of their true quality as they were picked apart by Portugal and barely threatened goalkeeper Diogo Costa, with Xherdan Shaqiri - their main hope of inspiration - rendered anonymous throughout.
Switzerland may regard reaching the knockout phase as par for the course at this tournament but there must still be huge disappointment at the meek and mediocre manner in which they have left Qatar, because previous evidence suggests they are a much better side than the one thrashed here.
-- Courtesy of BBC Sport