Is Wayne Rooney a good manager? There is an obvious answer to this, three jobs, three years and three abrupt departures into his career as a head coach, the latest that unremittingly disastrous 15-game spell at Birmingham City. And that answer is quite clearly: no. Nothing to see here. Move along please.

On the other hand, any assessment of Rooney’s capacity as a manager has one key flaw, what we might call a Wayne-22 situation, which states that Wayne Rooney has only ever been employed as a manager by the kind of board that thinks it’s a good idea to employ Wayne Rooney as a manager.

Related: Wayne Rooney sacked as Birmingham manager after just 15 games in charge

This is the basic paradox here, the Wayne-as-Groucho scenario. Any club that can weigh up all the facts and still conclude that Rooney is the answer: this is exactly the kind of club Rooney should avoid like the plague.

Understandably, Wayne has yet to take this self-limiting principle on board. Although in the case of Birmingham, there were a fair few giveaways from the start. For the club’s supporters this will be the real significance of a second managerial sacking in three months under the new ownership. Wayne may be gone. But the enablers of Wayne are still very much in the house.

Football loves a circular morality tale, and the story of Rooney and the Blues is at least one of these. His final act as manager was a bruising 3-0 defeat at Elland Road on New Year’s Day. Rewind to 12 August and the first home game under the ownership of Knighthead Capital was also against Leeds, a high-energy occasion gingered up by a razzmatazz of music and fireworks.

The home fans chanted “Yoo Ess Ay”. Knighthead’s co-founder Tom Wagner, the kind of magnetic, bald, middle-aged financier who talks a lot about “dynamic scenarios”, could be seen celebrating wildly in the directors’ box as Lukas Jutkiewicz scored a 91st-minute winner.

Fast forward to 9 October and John Eustace was fired as manager, a move justified with some blather about the need for “a culture of ambition” and “a no-fear playing style”, both of which were apparently present most obviously in the form of Rooney, whose previous managerial career offered zero hard evidence of either of these things.

As a neutral, it was hard not to want it to work. Rooney is a popular figure, deeply committed to succeeding as a coach. His appointment was also undeniably in keeping with that stated culture of razzmatazz. Except of course razzmatazz in the manager’s seat is generally asking for trouble.

Fast forward once again to Monday afternoon and Rooney was reduced to talking about Jimmy Savile chants and pleading with his own board – so often the managerial death rasp – for new players, before the inevitable reckoning up on Tuesday morning.

Those 15 games in charge were desperate stuff. Rooney’s Blues won two of them, failed to score on six occasions and went from sixth to 20th in the table. It is rare to have such an instant impact on any team, and even rarer for that impact to be so profoundly negative, to the extent it is hard to think of many more obvious acts of mid-season self-harm by any club board.

What happened here, exactly? There has been a suggestion from journalists close to the club of a mismatch of method and reality, of players weighed down by an excess of information and tactical blueprints. Where Eustace had excelled at working with a relatively limited squad (net transfer spend in the last three years: £1m) Rooney came with no experience of success on a shoestring.

And there will, of course, be a degree of told-you-so at this outcome, even something oddly reassuring. Empty glitz, corporate disruptor-chat, Tom Brady presented as a kind of shiny celebrity trinket to dazzle the fawning locals. English football can still revolt against this kind of thing.

The Rooney interlude is in its own way a tick for the Championship, for its status as a hard-edged sporting competition. The culture is more robust than this, as various hedge-fund gunslingers have already discovered at Premier League level.

Not that English football should start feeling too good about any of this. Rooney’s failure to make a mark as a head coach, while continuing to find work as a head coach, is in keeping with a more localised culture of entitlement and celebrity fawning. Specifically the ongoing failure of the Golden Generation crop of players to succeed in management.

This is probably an overstated phenomenon. Most managers fail. The Goldens were a pretty small circle of celebrity footballers. But the fact remains that Gareth Southgate is still the only member of England’s World Cup squads 1998-2006 to have had any sustained success in elite management. Only last week Steven Gerrard could be heard urging the owners of Al-Ettifaq to finally get their wallets out or risk failing to maximise his own managerial brilliance. Gary Neville has spoken about his own – in retrospect quite obvious – lack of readiness for the Valencia job. Phil Neville is still out there doing Phil Neville things.

Frank Lampard has twice been appointed as a Premier League manager on a whim, and in the process successfully combined generous offers of employment with an ability to whinge about insufficient grace, favour, patience and/or the weakness of his players; basically everything other than his own capacity to do the job.

If there is a tendency to linger on these failures, this is perhaps related to the fact that group of players were the first to really make the leap up, to become powerful, wealthy and genuinely famous, independent of the game’s older structures. It was always going to be tempting to see hubris in their subsequent failure to win everything all the time (the golden tag was always overstated: they were pretty good). And to see the same vices now in their coaching failures, the same qualities of entitlement and tactical bluntness, the obsession with celebrity that circled their time as England players.

But there is, of course, a more state-of-the-art meeting of cultures here. Rooney’s appointment at Birmingham by a US ownership fixated with commercial opportunities speaks very much to the present and indeed the future.

The manager may be gone but the “vision” remains in place, as does the CEO who hired him, the same Garry Cook whose career was made by his successes in brand-building with Nike, who once talked up Thaksin Shinawatra’s credentials as a golf partner and all-round good guy; who has, since his time at Manchester City, been doing stuff for UFC and the Saudi Pro League; and who announced on his arrival at Birmingham “we aim to be world class in everything that we do”.

How’s that working out so far? Perhaps the best move City could make would be to re-hire Eustace, who seems ideally placed to fix the mess caused by his own departure. Back in the real world Gary Rowett, sacked by the previous board to accommodate a previous celebrity meltdown in the form of Gianfranco Zola, is said to be at least close to the frame. As for Rooney, who is no fool, and who is desperate to succeed, it is hard to write him off as manager just yet, or to say he has definitively failed; if only because every job so far has been a Wayne Rooney job.