Sir Dave Brailsford was born in Derbyshire and brought up in Wales. He lives in Nottingham, works in Manchester and supports Liverpool. But he has an international outlook, perhaps the product of taking himself off to France in his late teens to pursue a career as a semi-pro bike racer. So it was no real surprise to hear the Team Sky principal say, when asked this week to identify his next ambition, that it would be nice to win the Tour de France with a French rider.

He rowed back on it a bit the following day, under further questioning. But he had indeed said those words and they were consistent with everything we know about a man who, over the past decade, has made himself Britain’s most successful and admired sports leader. Brailsford is a man without frontiers.

His statement also revived the debate over the nature of Team Sky. Is it essentially a British team, dedicated to advancing the cause of homegrown riders? If so, why were Bradley Wiggins, Peter Kennaugh and Ben Swift not included in the squad for the 2014 Tour, alongside riders from Spain, Austria and Belarus? The debate intensified on Wednesday when a badly bruised Chris Froome left the race, the Kenyan-born 2013 champion handing over the team leadership to Richie Porte of Tasmania rather than to the only Briton left in the team, Geraint Thomas of Wales.

Had Wiggins been selected, Brailsford’s critics said, the Englishman would have been ideally placed to pick up the baton. And Kennaugh, crowned British road race champion a few days before the start of the Tour, confirmed his class by spending this week in the leader’s yellow jersey at the demanding Tour of Austria.

The reason for omitting Wiggins was that Froome does not trust him. But although Brailsford is a man who would rather learn from high-profile mistakes than hide behind a more conservative strategy, his failure to integrate the past two Tour winners into the same nine-man team was exposed as this week’s events unfolded on the Flanders cobbles, where Wiggins performed impressively during the Paris-Roubaix classic in April.

When Brailsford attended the unveiling of the 2014 route in Paris last October and saw the inclusion of a section of Paris-Roubaix, he must have foreseen the possibility of such an outcome. Froome is not the greatest bike handler. He crashes quite a lot, and sometimes at strange moments. In the under-23 world time trial championship in 2006 he rode down the starting ramp and straight into a marshal. Competing in Paris-Roubaix two years later, he slammed into the back of a commissaire’s car. At last year’s Tour he toppled into the barriers at the start of stage one, before the racing had even begun. This week he came down on Tuesday, damaging his wrist, and gave up after falling twice more on Wednesday.

Suddenly the most likely heir to his crown seemed to be Vincenzo Nibali, who took control of the race in Sheffield and looked completely at ease on the wet cobbles. Brailsford was keen to sign Nibali during Sky’s early days and in Paris last autumn he talked about the Sicilian in terms suggesting that he had already worked out what might be in store this week. “What I like about Vincenzo is that he’s a real cyclist,” he said. “He’s a fighter, he’s aggressive, and he never gives up. On the cobbles he’s a better rider than Froome.”

Even as Sky’s designated leader was making plans to fly home to Monaco on Wednesday night, Brailsford was expressing his enjoyment of the day’s racing. “It might not have worked out for us,” he said, “but if you watched what Nibali did today, you’ll remember it for a long time.”

Brailsford probably has a little more time to enjoy such sights since announcing earlier this year that he was relinquishing his role as the performance director of British Cycling, the national governing body, in order to concentrate on his work with Team Sky. But the fact remains that the professional team was built on the foundations of British Cycling’s Olympic programme, supported both by the subscriptions of its membership – 15,000 in 2004, 93,000 today – and by lottery funding.

When James Murdoch started signing the cheques for Team Sky, he was benefiting from an already highly evolved infrastructure. For five years Brailsford has straddled the two operations, and in 2011 a Deloitte investigation into possible conflicts of interest found “no major risks or issues”. A remarkable run of success on both sides of the operation – gold medals for Team GB, yellow and green jerseys for Team Sky – encouraged the growth of an army of British fans, whose enthusiasm was on show from Leeds to London last weekend.

Much of that enthusiasm was generated by the patriotism stirred when Wiggins and Mark Cavendish beat the world in a sport not previously notable for British success. The question now is whether Brailsford maintains a responsibility to nurture their successors or whether, like some Formula One marques, Team Sky is blind to nationality.

Brailsford often says that tough decisions, such as the one to bar Wiggins from the Tour, are best made by removing emotion from the equation. But once you take human emotions out of sport, you lose the feeling he got from watching Nibali’s performance this week. You can only spend so long applauding a machine.