Hundreds of huge white plates lie scattered along the roadside in the centre of Doha, Qatar, as if someone has had a spectacular accident with a gigantic crockery cupboard. The creamy discs tilt this way and that, colliding with each other in a random muddle along the edge of the highway, forming an otherworldly landscape of canopies, terraces and enigmatic slit windows.

This pile-up of flying saucers is the new National Museum of Qatar, an astonishing creation by French architect Jean Nouvel, and the latest supercharged volley in the Gulf states’ cultural arms race. Two years ago, Nouvel unveiled the glistening upturned colander of the Louvre Abu Dhabi. Now he’s back with another gargantuan palace for the Emirates’ arch rival. In its sprawling nearly mile-long loop of galleries, the museum tells the story of how this tiny nation of nomadic bedouins and pearl divers became, with the discovery of natural gas, the most wealthy country per capita on Earth in just 50 years.

“Architecture is the testimony of an epoch,” says Nouvel, wearing his trademark black leather jacket and wide-brimmed black hat and standing beneath his soaring concrete discs. “This building is a testimony of this moment in Qatar – a very, very powerful period that has seen a very strong mutation.”

Looping galleries … inside the museum. Photograph: Danica O Kus

The gas-rich state’s phenomenal influence is evident the world over. In London, Qatar now owns more land than the Queen, having snapped up everything from Canary Wharf and the Shard, to the Olympic Village, Chelsea Barracks and Elephant and Castle – along with Harrods as the crowning jewel in its luxury portfolio. Its foreign investments range from banks to universities, while its buying power in the global art market is unmatched. So what form did Nouvel think would best embody this miraculous national story? What kind of monument could represent the world epicentre of soft power?

His first impulse was to bury the entire complex below the ground. Perhaps unsurprisingly, this didn’t go down too well with his client, who was looking for something rather more visible. Charged with conjuring a spectacular, unrepeatable form, his team went back to the drawing board and drew inspiration from a “desert rose”, an intricate rock formation created when minerals crystallise in the crumbly soil just below the surface of a shallow salt basin. “It is a form created by the desert and time, a structure of endless intersections,” says Nouvel. “It is totally irrational. And it was difficult, because no one knows what it looks like inside.”

The museum surrounded by Qatar’s skyscrapers. Photograph: Iwan Baan/AFP/Getty Images

The resulting supersized sand crystal grows out of an early 1900s royal palace on the site, extending in a virulent cluster to envelop a central courtyard – a nod to the region’s caravanserai buildings, where travellers would unload their wares. As the strange mineral apparition multiplies around the site, the discs take on different roles: one rises from the ground, forming a sloping terrace with great views across the bay; others project to provide much-needed shade. Barely anything about the museum is legible as a conventional building. Every part is made from the collision of intersecting discs, giving it the surreal object-like quality of a Claes Oldenburg sculpture.

Eighteen years in the making, the National Museum of Qatar was a fiendishly complex idea to realise. The 539 discs are clad with 76,000 glass-fibre-reinforced concrete panels, requiring a level of technical gymnastics only made possible by software developed by Frank Gehry’s office (and a construction budget of more than $400m). Unlike much computer-generated blobitecture, the museum has a geometric rigour and rugged material heft, as if it could have been grown from the ground. It balances the rough with the smooth: while the discs have a crystalline precision, tapering to razor-sharp edges, the courtyard has been left with a pleasingly sandy surface, as though ready to host a caravan of itinerant traders.

In stitches … a Baroda carpet in the Pearls and Celebrations gallery. Photograph: Danica O Kus

Step inside and it feels like entering a geological chasm. The angled plates create a labyrinthine experience, with ceilings soaring up above lofty lobbies, before plunging down to create intimate nooks and crannies. The spatial drama is amplified by the fact that the floor is also made of subtly ramped planes, drawing you through the galleries in a gradual slope. Nouvel says he got the idea from his mentor, Claude Parent, who imagined a radical future where all buildings would be composed of steeply sloping surfaces – a heady vision that is not without practical drawbacks.

“Jean’s architecture is incredible,” said Sheikha al-Mayassa bint Hamad bin Khalifa Al-Thani, chair of Qatar Museums, “but the walls make it very difficult to hang anything.” As a result, the exhibition format relies heavily on immersive projections that cover most of the walls, providing an animated backdrop to more conventional dioramas and displays of objects in vitrines.

Beginning with a 400-million-year-old fossilised fish, the loop of 11 galleries moves from the natural history of Qatar’s geology and wildlife, to archaeology, cultural traditions and pearl fishing, as well as the momentous discovery of oil and gas that changed everything. The family lineage of sheikhs is dutifully celebrated, too, with cases of their personal effects and medals bestowed by foreign nations.

Some Nepalese labourers employed at the museum said they were paid a much lower salary than promised

The displays are generally well put together, but for now it all feels too sparse, the gaping rooms conceived for a collection that is incapable of filling them. The highlight is found in a side gallery, in the form of a temporary exhibition deftly curated by Dutch practice OMA and local architect Fatma al-Sahlawi, which puts Doha’s extraordinary building boom in much-needed context. It documents the early city masterplans to the present context, charting how 11 Pritzker prize winners have been hired to shape Qatar’s identity with evermore elaborate visions.

But what’s missing throughout the museum is any confrontation of the more painful side-effects of this rapid growth. Unlike at the city’s eye-opening slavery museum nearby, the sensitive territory of human rights is left well alone throughout.

It is a topic that this worldly nation should be more willing to confront head on. In 2016, a Guardian investigation into construction workers’ conditions in Qatar found alleged abuses ranging from irregular or decreased payment of wages to passport confiscation and high levels of debt bondage. Some Nepalese labourers employed at the national museum said they were paid a much lower salary than promised when they were recruited in their home country.

Is this the 400-million-year-old fish? … a gallery of desert artefacts. Photograph: STR/EPA

Facing increased international scrutiny in the run-up to the 2022 World Cup, Qatar has now introduced a minimum wage for migrant workers and says it is trying to replace the kafala (sponsorship) system with a new contractual system, and bar employers from confiscating workers’ passports. But for campaign groups like Human Rights Watch (HRW), the reforms don’t go far enough.

“While Qatar has taken some important steps to protect human rights, there is still a long way to go before migrant workers are protected from abuse and exploitation,” HRW’s deputy Middle East director Lama Fakih said in January. “As Qatar races to complete planned construction projects in time, now is the time to put in place durable labour rights reforms.”

The museum’s final gallery, set to focus on modern-day Qatar, is yet to be filled. The human costs of the country’s insatiable ambitions would be a worthy subject.