By the work of fate and the fixtures software, Manchester United visit Liverpool on Sunday, the first Anfield match since the Hillsborough Independent Panel conclusively vindicated the bereaved families' 23-year struggle for the truth about the disaster to be accepted. There are some worries, claiming far too much attention, about whether everybody among the 45,000 people in attendance will find it in their moral souls to respect the memories of 96 fellow football supporters who died in the grotesque negligence of Hillsborough in 1989. But football, so great a spectacle, has always been good at its grand moments of reconciliation.

On Sunday the two captains, Steven Gerrard and Nemanja Vidic, will walk together and release 96 balloons, to float into the Liverpool sky in remembrance of those supporters, all loved and mostly young, whose deaths make up that still unthinkably large number. Surely in this context Luis Suárez will then shake Patrice Evra's hand as required and finally end the hostilities between them.

The minute's silence, the black armband, the laying of a wreath: football has refined its ritual remembering of the disasters that pockmark its rise to local and global pre-eminence. For the most part, as with the minute's silence held by the modern-day, different Sheffield Wednesday this week before their Championship match with Huddersfield Town, all supporters in the crowd do observe the moment. But then the whistle blows, and the game hurtles on.

Too often the deeper challenges posed by the tragic event being remembered are forgotten, or discarded. Hillsborough itself was a watershed, for the end of English football's bad old ways, but much of the spirit in Lord Justice Taylor's landmark reports – there were two – were ignored. His analysis was about much more than all-seat stadiums, and concluded with this: "After the horror of Hillsborough … the lesson is surely that now is the moment for the fullest reassessment of policy for the game."

In the 10 days since Taylor's first report, on the causes of the 1989 disaster, has finally been acknowledged as the truth, there have been some signs that football's response may just be shaping into a lasting legacy.

There was real feeling in the beautifully staged tribute to the 96 by Everton before their game against Newcastle United, an understatement in the "He ain't heavy, he's my brother" lesson, that sport should unite us all, not curdle into vitriol. Yet if this moment is to be a watershed too, football will need to think about it all for longer than this week, for more than just a minute.

In his second report, the one people in football do recall, on safety in sports grounds generally, Taylor insisted on laws to change the dismal culture, in which supporters huddled in sordid, unsafe conditions while the directors feasted in their lounges. He insisted stringent safety standards be made compulsory – along with his all-seat stadium recommendation many fans still believe was unnecessary – because after serial disasters the men who ran football could no longer be trusted. Taylor noted the "massive public support and interest" the national game commanded, despite the dreadful problems then disfiguring it; the crowds, which mostly braved it then only at the big games, were waiting to flock back.

In his observation of football's boardrooms, as astute as his slicing through the lies of South Yorkshire police, Taylor famously noted: "As for the clubs, it is legitimate to wonder whether the directors are genuinely interested in the welfare of their grass roots supporters. Boardroom struggles for power, wheeler-dealing in the buying and selling of shares, and indeed of whole clubs, sometimes suggest that those involved are more interested in the personal financial benefits or social status of being a director."

It is one of the great contradictions in football's modern history that partly due to the rehabilitation Taylor himself ushered in, the directors then indulged in more "wheeler dealing in the buying and selling of shares, and indeed of whole clubs" than ever before. It is not difficult to imagine what Taylor would have thought of the £90m pocketed by David Moores for his shares in Liverpool, and £93m by Martin Edwards at Manchester United, for "wheeler dealing" in their shares. That has led to the bizarre position of two great clubs, entrusted with so huge a responsibility for setting the tone tomorrow, being owned by faraway Americans who knew nothing of the sacrifice that built English football, but were attracted by the dollars in the TV rights.

As many supporters know, Taylor decided to back the government's, the FA's and top clubs' desires for all-seat stadiums, but recommended they should not raise prices for the supporters who had stuck with the game through the 1980s. The Football Supporters Association argued that the clubs would do so but Taylor, despite having identified the venality in directors, said they need not, pointing to the then £6 price of a seat at Rangers' Ibrox. What has happened since, the £45 charged now for a seat on what was once Liverpool's fabled standing area, the Kop, has proved that the fans knew their clubs rather better than did the judge.

Conditions for supporters have, of course, been hugely improved and the game has been greatly refurbished. There have been many changes, but that "fullest reassessment of policy" never really happened. As football was rehabilitated, the clubs were allowed to raise prices beyond the reach of the next generation.

It is a grim truth that so many of the Hillsborough victims were teenagers because then, at £6 a ticket for the Leppings Lane end, they could afford to be part of the game which then failed them so abysmally. The clubs have developed community work vastly more sophisticated than anything envisaged in 1989, but they work with "socially excluded" young people whose exclusion extends to the stadium, too, priced out of what was once validly called "the people's game".

The truth about Hillsborough has broken through, as the poet laureate, Carol Ann Duffy, wrote for the Liverpool Echo, like the sweet silver song of the lark. So perhaps now is the time for that full reassessment, not just for a minute.

And if the fans, who watch these modern, overseas-owned corporations we still call clubs, in much better conditions, might have their own reassessment, it goes beyond ending pathetic chants burped up by ignoramuses who do not deserve the airtime. It should be to reclaim, somehow, the way football was supported for decades, when fans of rival clubs might like a drink and be tough enough, but would walk together and watch together without needing segregation. When the Munich air crash happened in 1958, there was great solidarity around football. The sad little song mocking it only wormed in with other rubbish behaviour, years later.

Twenty-three years after the first Taylor report, its truth is finally accepted. It has felt as if Liverpool, the country, and football as a whole have breathed a mighty sigh of relief with the bereaved Hillsborough families. So football may now remember the spirit of the second Taylor report, not just the bits the clubs wanted, and, as the balloons lift to the heavens before this grandest of fixtures, think of an all-round better way for the game.