Manchester United will not see themselves as mugs for paying a world record fee to buy back a player who was on their books four years ago. Instead, their marketing men can present the purchase of Paul Pogba, who signed a five-year deal late on Monday night, as evidence of the club’s enduring power and prestige. United are not in the Champions League this season, but they have ensured, by adding Pogba to a box-office cast that includes José Mourinho and Zlatan Ibrahimovic, they remain more interesting than many clubs who are. That’s showbiz, in which United have a specific role to play. Outbidding Real Madrid is at least as important to them as outperforming Leicester City.

Last season’s sensational Premier League winners may have been applauded for their mostly frugal recruitment, but, by contrast, there is a sense that bargain-hunting would not be becoming of United in their present diminished sporting state. Sometimes, for some clubs, buyers’ remorse is caused by not spending extravagantly. Hark, is that wailing Arsenal fans you hear? Yes it is. Their club is as permanent a part of the Champions League draw as banal interviews and they have finished above United in the past three Premier League seasons, yet the activity of the summer so far makes many Arsenal fans view United as more in tune with the times, with disenchanted Gooners yearning for a big-name recruit.

It has got to the stage that even if Arsène Wenger didn’t believe that a particular star could improve his team, it might be worth signing him just to enhance the mood around Arsenal, as a kind of marquee placebo.

Pogba, in fairness, is more than just a glamour signing who shows that United, and the Premier League, are wrestling some pulling power back from European rivals, notably Spain’s swoonsome hunks. This is a trophy recruit who could also help land trophies. Indeed, the fact he is every bit as image-conscious as United could help give more substance to his status; the size of the fee is unlikely to be a millstone around the neck of a player who, like Cristiano Ronaldo before him, has always believed he has what it takes to become the greatest and seems reinforced by others’ confirmation.

It is true that he has not shone in the two biggest events of his career – the recent European Championship in France and the 2015 Champions League final – but he has proven emphatically that he was right to leave United four years ago and seems well equipped to vindicate United’s decision to bring him back, having developed physically, technically and tactically.

He does not have the ingenuity of Diego Maradona or the lawless wit of Luis Suárez, so does not cast spells over opponents, but he has shown that he can certainly help subdue them and uplift his team. He can help fill a United centre that has been hollow for too long.

It will be fascinating to see exactly how Mourinho deploys him. While the size of the transfer fee signalled the continuing degradation of international football, insofar as it showed that tournaments such as the European Championship have dwindling relevance to players’ values (no matter what Newcastle United may tell suitors of Moussa Sissoko), Mourinho might have found value in seeing Pogba’s influence curbed by the relatively restrictive role assigned to him by Didier Deschamps at Euro 2016. United would do well to let Pogba move and attack with the sort of freedom he enjoyed at Juventus.

The Juventus manager, Massimiliano Allegri, previously tried to sign Henrikh Mkhitaryan to revel with Pogba in Turin. Now United have that pair it is possible that they could thrive as two parts of a central trio in a 4-3-3 scheme, although Mkhitaryan may instead be used wide on the right, where none of the alternatives – Juan Mata, Jesse Lingard or Memphis Depay – have all the traits that would obviously endear them to Mourinho. The calibre of player vying to accompany Pogba in the centre remains open to debate, as question marks of varying weights hang like cartoon anvils over Morgan Schneiderlin, Daley Blind, Marouane Fellaini, Ander Herrera and Michael Carrick, and, as Mourinho did not quite say this month, only a fool, or perhaps a recently deposed England manager, would attempt to foist a dwindling Wayne Rooney on United’s midfield.

A position out wide is out of the question for Rooney and with Marcus Rashford and Anthony Martial on the rise, it is hard to see where else he could fit in up front, unless Ibrahimovic, seemingly a young 34 to Rooney’s old 30, turns out to be a flop, albeit a usefully spectacular one.

If United’s world-record capture of Pogba is a demonstration of the club’s glow and ambition, it also highlights further the obsolescence of a man who will have precious few opportunities to collect the five goals he needs to overtake Sir Bobby Charlton as United’s all-time record goalscorer. Chances are, however, that he will still be given enough opportunity to achieve that honour, which will add extra lustre to United’s roster.

Doubts linger about the strength of the new spine being built at Old Trafford by Mourinho (the sturdiness of the central defence is among the unknowns at this point, with much hinging on the recently recruited Eric Bailly). Although they have set a new benchmark for expenditure, their readiness to win a major title is questionable. But Pogba’s arrival certainly makes them stronger and more intriguing, which makes his purchase good business.