David Conn: The World Cup was a triumph. Now reform Fifa

Football makes Fifa powerful. We have a right to know that the people wielding that power aren't crooks

It's all over now. Four weeks of glorious telly and legitimised skiving, all finished in Yokohama on Sunday, with Cafu, Brazil's monumental captain, climbing on to the plinth and holding the World Cup in his hands, as if born to the role. The tournament has proved again for its governing body Fifa the global pre-eminence of football.

No other game – no other entertainment – has the power to captivate so much of the world, to glue more than a billion people to their televisions, from Copacabana beach to school assemblies in Pontefract and East Grinstead.

Yet in all the hours, weeks, of coverage by all media, who granted Beckham's toe and Owen's thigh more significance than the nuclear stand-off between India and Pakistan, there was almost no mission to explain this phenomenon, only to report it breathlessly and let its scale and spectacle speak for itself. Quite how football has so completely conquered the world, why old ladies here with a lifetime's disdain for the game found themselves discussing Nigeria's midfield in the hairdressers, nobody tried an answer.

As for other questions, especially those about corruption and bribery at Fifa and about its president Sepp Blatter, these were barely mentioned. Barry Davies, the BBC commentator who makes some claim to a cultural hinterland, began half-heartedly to trace the allegations against Blatter during one of the early games, then gave up. His co-commentator, the sheepskin-wearing John Motson, opened his coverage of the England v Argentina match by saying: "There may be more important things than this going on in the world, but I can't think of them."

Along with "Motty", the world forgot its troubles and settled back in its collective sofa to watch the show. At the end, on Sunday, there was Blatter, his grin as bright as the floodlights, gladhanding the Brazilians alongside Pele and Lennart Johannsen, the head of European football who has failed to unseat Blatter after years of trying.

It's legitimate to ask why it matters, the fetid smells coming out of Fifa's offices, general secretary Michel Zen-Ruffinen's dossier of corruption allegations against Blatter, which were lodged with a Swiss Court. Blatter's supporters are alleged to have offered cash for votes for his presidency in 1998 and this year, and he is alleged to have favoured his croneys with money and contracts, and to be misrepresenting Fifa's accounts, which David Will, a Scottish official not previously noted for subversion, claims show Fifa is insolvent.

But while the newswires fizzed with all this before the tournament, most football fans struggled to care. Two days before the World Cup began, Blatter was resoundingly re-elected. A new Fifa committee withdrew the legal action inspired by the corruption allegations, and Zen-Ruffinen was handed a nice, Swiss P45. France and Senegal kicked off, the world painted its face and analysis was put on hold. The questions have to be asked again now, and they have to be answered. Why? Precisely because the game is so phenomenally popular. Its power in a globalised age makes Fifa itself immensely powerful. We are entitled to know that the people wielding such power are, at least, not crooks.

Governments fawn over Fifa, like our own only 18 months ago, when Tony Blair had Blatter to tea and appointed a personal "envoy", Tony Banks, to support the FA's doomed, embarrassing bid to host the 2006 World Cup here.

Fifa preaches morality and world togetherness: "For the good of the game" and "the football family" are Blatterisms of choice. This self-righteousness is pushed along with McDonald's, Coca-Cola and Fifa's other multinational sponsor "partners", into every corner of the world. Honesty matters because it's massive business: for all the chaos, Fifa still received half a billion pounds for the World Cup TV rights, £140m from the sponsors. It'd be nice for the fans – and relevant to how well their game is run – to know the money is properly accounted for and spent wisely. For the good of the game.

Looked at in the traditional way, Fifa, like all sport governing bodies, are – here's an old-fashioned word – custodians. Their presidents and vice-presidents and secretary generals and committee members are not supposed to be there to self-aggrandise or profiteer. They find themselves with temporary responsibility for administering a game treasured worldwide. They do not own it. Their job – and this should apply to our own, compromised FA and money-hungry club chairmen – is to look after the sport and pass it on healthy to the next generation. Everybody is entitled to see that happens, and for allegations to be investigated.

Will it happen? Unlikely. This time even a whistle-blowing general secretary and a huge effort from Europe couldn't shift Blatter. He romped home, voted in by football bodies worldwide, many unaccountable, who are paid $1m a year by Fifa for development programmes. A majority likes the status quo.

The prospects are that Blatter, a consummate operator, will maintain his hold on Fifa, while European football, which is anyway resented for its great wealth, huffs and puffs. Expect more revelations, more rows, more front from Blatter. And then, in four years' time, expect the world to be reminded again that it doesn't really care enough.

davidconn@freeuk.com