In 2011, Banana Republic launched an official “Mad Men” range aimed at customers nostalgic for a more stylish time when they could drink so much before 2pm that they needed a nap. The centrepiece were those classic Don Draper hats: feathered fedoras and crumpled trilbies you could doff to your lift attendant. There was even a straw fedora, perfect for disappearing to Los Angeles for two weeks without telling the wife or kids where you were.

The range was a huge success, selling out completely, and the company’s annual reports started to sing about rising revenues. Banana Republic released new Mad Men collections for the following three years. But, today, its UK website has only a single hat for men – a wool felt baseball cap.

A Mad Men hat, previously available from Banana Republic. Photograph: Banana Republic

Indeed, it now seems as if the Mad Men fetishisation was the final hurrah for the man’s formal hat. An item that, a century ago, was as essential as trousers and shirts is close to death. It has entered a fashion black hole. Male celebrities have almost entirely stopped wearing hats, and those who still do really shouldn’t. Johnny Depp looks as if he is about to compere a slam poetry night in Tunbridge Wells, while Olly Murs looks as if he has been trapped in a children’s cartoon.

Summer is the perfect time to shelter under something large and floppy, but when I went into 10 major menswear stores at a Westfield shopping centre, in London this week – not one sold any hats apart from very casual iterations: caps, beanies and bucket hats. (Topman had a baker boy hat, somewhere between a flat cap and a Kangol beret, but it makes you look as if you are about to serve up school dinners.) Looking ahead to autumn/winter, it is the same story at trendsetting brands such as YMC, Ami and APC, which don’t have any non-casual hats as part of the new season’s ranges.

Caps and bucket hats have dominated Lanvin and Christopher Raeburn catwalks recently – and they were certainly on display everywhere in Westfield. The bucket hat re-emerged a few years ago on the hyper-stylish Swedish rap scene called cloud boys, after being sported by the scene’s leading light, Yung Lean. His fashion-conscious fans all began wearing bucket hats and the look spread to US rap, before becoming available at Urban Outfitters.

Notorious BIG in his trademark cap. Photograph: NY Daily News via Getty Images

But like so much of the current vogue for 90s sportswear, while the bucket is cool, it looks ridiculous on anyone over 21. You can probably get away with caps and beanies until you are 30, but after that you look like an undercover cop trying to bust secondary school drug dealers. So what are you supposed to do after that? Are hats out of the question?

This is a particularly important question for me because, as a bald man, hats are not just an accessory but a necessity. In the sunshine, my head sweats and peels. In the cold, each gust of wind feels like a dementor frenching my scalp. I’m 28, so on the verge of no longer being able to wear baseball caps and beanies. I would love to graduate to a smarter hat, but every time I try one on – for a wedding, for example – I feel like the sort of person who takes a guitar to the beach.

I speak to a couple of fashion experts who agree that formal hats conjure up unpleasant associations. Daryoush Haj-Najafi, a menswear writer and lecturer, says trilbies make him think of “Bacardi adverts”. Estefania Hageman, a stylist for menswear magazines, says the cap’s rise and the formal hat’s decline is part of a wider shift towards street culture. Skate brands such as Palace and Supreme dominate, while rappers such as Travis Scott and A$AP Rocky have become fashion icons. “We’re living in a moment that’s pure domination by hip-hop,” says Haj-Najafi. “The baseball cap is a New York item – hip-hop is from New York.”

Once a hat was a necessity … fans at a football match in 1919. Photograph: Popperfoto/Getty Images

Virgil Abloh is a leading light in men’s fashion who started outside the fashion world, working with hip-hop artists such as Kanye West and Skepta, designing tracksuits and trucker hats. In six years, he has gone from Chicago DJ to the creative director of Louis Vuitton. “He’s taken items like the tracksuit and baseball cap and made them high end and desirable,” says Hageman. Now even CEOs are wearing baseball caps – it’s the everyman look.” Essentially, men’s fashion now is about a lack of formality and caps fit into that, but trilbies don’t.

A hundred years ago, a hat was essential everyday wear for men, rich or poor. Photographs of football matches in the 1930s show every supporter wearing a hat. As styles became more relaxed after the war, hats fell out of favour for everyday, but were still a mainstay of fashion and celebrity – Michael Jackson’s black fedora, the Thin White Duke’s wide-rimmed boater, the ska scene’s adoption of the pork pie and the Notorious BIG’s Kangol 504 flat caps and berets. Even late in the early 00s, tween pop stars such as Justin Timberlake wore ridiculous hats as part of their effervescent sex appeal.

Pete Doherty has to take much of the blame for the demise of the formal hat. Photograph: Shirlaine Forrest/Getty Images

So, how were formal hats turned from an absolute necessity to an eyesore? Much of the blame has to be pinned on two men: Pete Doherty and Neil Strauss. Strauss is the author of The Game, a book that reports on and proselytises for the pick-up-community. Pick-up artists believe men can learn techniques that will make any woman sleep with them. One such technique is “peacocking” – wearing a few items of garish clothing to get you noticed and give you something to talk about. Hats were a big part of this, and became emblematic of a certain kind of sleazy nightclub-botherer – someone who would affectedly drink whiskey sours and lightly gesture toward the groin in the belief that they were subconsciously making women think about sex.

At the same time, the hat was having a real resurgence on the indie rock scene. Doherty led a small battalion, with Alex Zane, Peanut from Kaiser Chiefs and assorted members of the Australian band Jet bringing up the rear. Hedi Slimane, then the head of Dior Homme, was obsessed with Doherty and, together, the two men reimagined the male silhouette as something svelte, in tight jeans and a leather jacket, with a big protruding hat on top.

Over time, places such as Camden in London and the Northern Quarter in Manchester became overrun with men leering about in a trilby. That’s how the hat has become unchic: 10 years ago, it recalled a time of Madison Avenue manliness or troubadourish artistry. Now, it recalls a time when lads at V Festival with fags hanging out of their mouths were shouting: “Imogen, babes, don’t storm off like that!”

It wouldn’t be so bad if caps and beanies were a reasonable replacement. But most beanies look ridiculous (especially in summer); either too large or too small. Baseball caps are structured awfully, with big jutting rims that make you look like a train driver. I have a few that I love, including one from Weekday that I have bought three times and lost three times already, but it’s not easy.

Buckle up: the baseball cap gets a new look at the Dior Homme spring/summer 2019 show at Paris men’s fashion week. Photograph: WWD/Rex/Shutterstock

Still, there are some nascent signs that the baseball cap might be entering a stylish new phase. Arket has light seersucker versions, which its head of menswear tells me “compliment our idea of the everyday uniform” by focusing on “soft and natural materials”. You can see what he means - it’s a cap you could imagine wearing to a posh lunch. Cos and Topman are already stocking brimless versions – and there is a kind of workmanlike smartness to them, the sort of thing you could wear into your mid-40s and get away with.

Dior Homme’s spring collection for next year, which is inspired by formal wear, includes extremely smart baseball caps with ornamental buckles. The trilby, the fedora, the pork pie: there is no hope for these hats unless you want to repel your friends and lovers. But perhaps the smart hat’s return could come through the backdoor left open by sportswear.