Did you know that, if things had gone differently, the Pompidou Centre could have been an egg? In the 1969 competition for the Paris art centre – ultimately won by Richard Rogers and Renzo Piano, with their inside-out symphony of pipework – a radical French architect called André Bruyère submitted a proposal for a gigantic ovoid tower. His bulbous building would have risen 100 metres above the city’s streets, clad in shimmering scales of alabaster, glass and concrete, its walls swelling out in a curvaceous riposte to the tyranny of the straight line.

“Time,” Bruyère declared, “instead of being linear, like the straight streets and vertical skyscrapers, will become oval, in tune with the egg.” His hallowed Oeuf would be held aloft on three chunky legs, while a monorail would pierce the facade and circle through the structure along a sinuous floating ribbon. The atrium was to take the form of an enclosed globe, like a yolk.

Sadly, it wasn’t to be. His ovular poetry didn’t impress the judges and Paris got its high-tech hymn to plumbing instead.

L’Oeuf de Pompidou is one of many astonishing schemes to feature in Atlas of Never Built Architecture, a bulging compendium of dashed hopes and broken dreams that charts a fascinating alternative universe of “what ifs”. It is a world of runners-up and second bests, an encyclopaedia of hubristic plans that were too big, expensive or weird to make it off the drawing board.

It features best laid plans that became victims of political coups and economic crises, alongside the megalomaniacal visions of toppled tyrants, and projects that were scuppered by budget shortfalls, natural disasters and even a plane crash. It is a calamitous catalogue of corruption, bankruptcy and death, as well as a memorial to the untold hours of wasted work and unpaid labour that architects endure. But it all makes for a highly entertaining romp through what the world might have looked like, had fate chosen a different path.

One spread depicts a fantastical vision of a pleasure island, where a needle-thin spire rises from the cone-shaped dome of an ornate pavilion, surrounded by lush gardens dotted with more glass domes. The central building is raised on a platform and engulfed by a reflecting pool, reached by a majestic spiral ramp, recalling the processional route to an ancient ziggurat. It looks like the glitzy dream of a wealthy desert petro-state. And it is – except that it’s not the work of a contemporary “starchitect” for the Gulf, but the vision of Frank Lloyd Wright, drawn up in 1957 for Baghdad.

Wright had been invited by King Faisal II to design an opera house for the city, alongside a range of other stars of the day, including Le Corbusier, Alvar Aalto, Gio Ponti and Walter Gropius, who had been commissioned to design universities, government buildings, sports complexes and other palaces of culture. On his descent into the airport, Wright noticed a long, thin island in the Tigris River – a location he thought preferable to the downtown site he had been allotted. “The island, Mr Wright, is yours,” replied the king.

As was his habit, Wright quickly expanded his brief, concocting an entire Plan for Greater Baghdad, which he dubbed Edena. Along with the opera house, there would be a civic auditorium, a planetarium, art museums, a grand bazaar, gardens, fountains and tiered highways, all wrought in the curving language of caliph-era Baghdad, known as the Round City, when it was surrounded by concentric circular walls. It would have been Wright’s grandest project by far – if the king had not been assassinated in a coup in 1958. The architect himself died the following year, aged 91.

The book’s two authors, Los Angeles-based architecture writers Sam Lubell and Greg Goldin, have foraged far and wide to compile a collection with impressive geographic scope and depth, beyond the usual suspects. Their research led to a “shortlist” of 5,000 projects, which they distilled to 1,000, then cut to 350 for the book – one of Phaidon’s hefty atlas tomes, weighing in at 1.5kg, with a £100 price tag.

The projects range from bold parliaments for African cities, to a futuristic hotel that would have hovered above Machu Picchu, as well as what the South Bank of the Thames might have looked like if the American PoMo doyen Philip Johnson had had his way (Answer: a cartoonish neo-brutalist fantasy of the Palace of Westminster, teeming with crenelated towers.) There are plenty of plans that didn’t materialise the first time around, but later realised elsewhere, as well as ideas that were far ahead of their time, but now prove to be unnervingly prescient.

One was Hungarian-French artist Nicolas Schöffer’s Tour Lumière Cybernétique. This illuminated beacon would have been an interactive multimedia answer to the Eiffel Tower, a skyscraper-sized smartphone designed to broadcast a barrage of notifications across the skyline. Bristling with arrays of loudspeakers, flashing lights, smoke signals, moving rods, rotating mirrors and more than 5,000 projectors, the tower was designed to relay data concerning the weather, traffic, news and even citizens’ movements.

Schöffer described it as “an intense living flame, constantly transformed and transformable”. He saw his beacon as a way to democratise information – which, he argued, was otherwise limited to those in control of government and production. But by the 1970s, the possibilities of cybernetics were increasingly seen as a menace, viewed as tools that would enable the invasion of privacy and limit personal freedoms. Schöffer’s tower might not have materialised, but its principles live on in the data-harvesting hubs of “smart cities”, less broadcast on public billboards than hidden away in anonymous data centres.

Towers appear throughout the book, this most ambitious of building types being the one most likely to come a cropper – and often triggering unintended consequences. The endurance of New York’s cherished neoclassical Grand Central Terminal, for example, is in part thanks to the backlash prompted by a 1954 plan to replace it with a 109-storey circular skyscraper. The hourglass-shaped design, by the Chinese-American architect IM Pei, was commissioned by Robert Young, then chairman of the ailing New York City Railroad, who thought that not exploiting the air rights above the historic station was as foolish as owning “a stretch of farmland worth $100bn and never putting a plough to it”.

Pei’s project, dubbed the Hyperboloid due to its twisting form, would have been the world’s tallest and most expensive building at the time. But, facing plummeting profits and a Senate investigation of the industry’s decline, Young killed himself in 1958, dashing any hopes for the tower. Meanwhile, opposition to the plans helped spark the modern preservation movement, seeing the beloved terminal bestowed with landmark status in 1967.

While Pei’s tower might have offered spectacular views over Manhattan, the same could probably not be said for the Indiana Tower, dreamed up by César Pelli in 1981. The Argentina-born architect, who would go on to design Kuala Lumpur’s iconic Petronas Towers, was brought in to conjure a landmark for Indianapolis to rival the St Louis Gateway Arch or Seattle’s Space Needle. His solution was a 228m-high obelisk of concrete and limestone, with a 2.8km walkway spiralling its way to the top, where visitors could look out across sprawling plains of Indiana farmland. “Like the Eiffel Tower in Europe, it will be the thing you must see,” Pelli claimed. “It will be known as well in Moscow as it is in Singapore!”

Locals were not so impressed. Some thought it looked too much like a corncob, cementing the stereotype of Indiana as a rural backwater. Others compared it to an oil derrick, while one appeals court judge said it looked like a bundle of chickenwire. “If you’re going to make it bad,” said the president of the local architects’ society, “don’t make it big.”

External consultants brought in to evaluate the viability of the project were equally blunt. “Structures you can get up in the top of and look out work in cities like Seattle,” they wrote, “where there are two mountain ranges and Puget Sound, but it may not be attractive in a midwestern location simply because there is not as much to see when you get up there.”

The Italian master Carlo Scarpa was sanguine about his many unrealised plans. Not building was possibly the only way to ensure peace. “It is better to do nothing,” he said, discussing his unbuilt Civic Theatre for Vicenza. “That way everyone will be happy: the city council, because it has avoided the criticism that can be directed at those who do something ... the opposition, because it can say that the administration does nothing, after trumpeting the theatre; those who do not want the theatre, because it will not be there; those who do want it, because they can continue to complain that there is no theatre; and meanwhile dreaming, each on his own, of an ideal theatre, made in his own image and likeness.”

Sometimes, the perfect project is better left in the imagination.

• Atlas of Never Built Architecture is published by Phaidon on 22 May 2024, £100