Ten days ago Leicester City, fuelled by their sheer terror of the implications of the relegation they appeared to be hurtling towards, sacked the man who had led them to the greatest moment in their history nine months previously. As of the start of this weekend none of the top 14 clubs in the Premier League had changed their manager this season, but four of the bottom six had, one of them twice. There is a systemic problem here, and it is not a new one. Helpfully, one of the greatest English managers of all time has looked into it and suggested a possible cure, and given his eminence it would seem remiss not to consider it. Even if he came to his conclusion 90 years ago.

At 9.30pm on 18 December 1926 Herbert Chapman, the manager of Arsenal, gave a talk on the radio entitled The Football Industry. It wasn’t what we might now consider classic Saturday evening entertainment, but with the first television broadcast still a decade away, pubs locking up as he got under way and only one English station to listen to, there were not exactly a lot of alternatives. So it was that millions heard him make proposals that Athletic News described as “more than startling, they are revolutionary” and “certainly courageous, if, as many may consider, fantastic” and briefly became the talk of the game.

Among them, Chapman suggested signings should be prohibited once the season started. “We kick off together, let us all run the race from scratch,” he said. “No buying new players; no getting fresh horses once we have left the post. Clubs have about four months to fit themselves for the race. It should be enough.” Some 76 years later, with the addition of a short bonus mid-season free-for-all, the transfer window was adopted.

His other key proposal looks less familiar, but the problem Chapman was trying to address most emphatically does not. The fear of relegation, he said, was forcing clubs to make short-sighted, rushed and often regrettable decisions, particularly in the transfer market. “It is this horrible bogey, this fear of descending into a supposedly lower grade of football, that is at the root of the transfer trouble,” he said. “Rightly or wrongly, relegation is looked upon as an almost insufferable indignity.”

Little has changed since then, except that we are now too childish to say “bogey” without sniggering. Although struggling teams will inevitably be tempted to change their manager – there is no reason for anyone to simply accept failure – there should be no need for them to be in such a rush. “If the pronouncement stirs clubs to consider again the present suicidal policy of paying more and more for new players – often under the compelling threat of relegation or the activities of wealthier rivals – a good purpose will have been served,” Athletic News concluded in their review of Chapman’s speech. “Sooner or later the knife will have to be used to this cancerous growth.”

The knife has yet to be wielded, and the cancer is still growing. Chapman went on to propose a novel cure, something that “would eradicate that feeling of disgrace attaching to the clubs relegated” and “do away with that fear of financial embarrassment”. It would, he suggested, have the additional benefit of adding intrigue to a top flight in which, for “the majority of clubs, interest begins to vanish with the coming of spring. Teams have been knocked out of the FA Cup, league honours are not likely to come their way. There is not even the morbid excitement of wondering if the club will escape relegation.

“Most of the clubs are virtually safe. It is stalemate. Nothing to fight for, nothing to struggle against.”

All that need be done, Chapman suggested, is to relegate half the division. “At present clubs know when they descend into the lower division that nothing but good luck and good fortune will get them back to the top class,” he said. “If 11 clubs were to go down the stigma would not be felt nearly so keenly. Clubs would have the comforting satisfaction of knowing that there would be an even chance of climbing back again within 12 months. A club would be very poor indeed which, having failed, did not succeed in getting back to its rightful class in less than three seasons.”

Chapman’s proposal would have benefits beyond easing the consequences of relegation. The number of new clubs arriving in the top flight each season would increase interest and would give many teams currently excluded a chance to stick their faces in the Premier League cash trough. Players who toil in relative obscurity, many of them English, while top-flight clubs overlook them in favour of seasoned internationals from elsewhere, would have a chance to prove themselves at a higher level, and perhaps to remain there.

Relegating fully 50% of the top flight is a tad excessive, but there is some merit in Chapman’s madness particularly as clubs continue to feel compelled to switch managers and make desperate forays in the transfer market, to their very great detriment if and when they go down regardless. But if five teams were to go down from the top flight the second tier might be transformed, and the Premier League largely unaffected (if Sunderland slip this year West Brom would become the only team to finish 16th or 17th in the 10 years to 2015 and not subsequently suffer relegation anyway). With two guaranteed promotion places, four lottery tickets and 21 shades of failure the Championship is simply too terrifying a prospect, and after nearly a century it is time to tart it up. Or of course the Premier League could start sharing their riches a little more equitably with the divisions below them, one idea they would be even less likely to accept than Chapman’s.

• This article was amended on 6 March 2017. An earlier version used the word “systematic” where “systemic” was meant.