Ever since Mexico City was founded on an island in the lake of Texcoco its inhabitants have dreamed of water: containing it, draining it and now retaining it.

Nezahualcoyotl, the illustrious lord of Texcoco, made his name constructing a dyke shielding Mexico City’s Aztec predecessor city of Tenochtitlan from flooding. The gravest threat to Mexico City’s existence came from a five-year flood starting in 1629, almost causing the city to be abandoned. Ironically now its surrounding lake system has been drained, the greatest threat to the city’s existence is probably the rapid decline of its overstressed aquifers.

No wonder water flows through many of Mexico’s City’s unbuilt projects.

The first plan to eliminate the city’s lakes while preserving canals and reservoirs for transport and irrigation was proposed by council member Francisco Gudiel in the 16th century. Gudiel’s vision was nixed by a city council unwilling to contribute the necessary funds. The lakes remained for a couple more centuries, disappearing just when the car came on the scene in the early 20th century. When they were finally drained no water was left for irrigation or transport and the city became a rapidly expanding maze of concrete, swamped with motor traffic.

The Aztlan 2000 project, from 1970, envisaged a huge social housing complex to accommodate migrants to the Mexican capital. Photograph: Secretaria de Obras Publicas

A ring road surrounding a grid of streets has been a central vision for Mexico City since the first modern urban development plan by Carlos Contreras in 1933. One proposal in this vein from Mexico’s ministry of works in 1967 would have heavily impacted the city’s urban landscape with a double ring road surrounding the city’s historic centre, one clockwise and one counterclockwise. Areas such as the Tepito and Merced neighbourhoods would have been filled with high-rise social housing for 80,000 people and high-value commerce. The plan disappeared silently when Mexico was engulfed by student protests in 1968.

A 1970 project from the ministry of works, called Aztlan 2000, envisioned the construction of a social housing complex for 1.5 million inhabitants in the city’s northern periphery to accommodate the masses of new migrants coming to the booming megalopolis. The plan integrated housing, malls, a racetrack, hospitals, a zoo, a golf course, a stadium, a subway and a museum, among other amenities. None of these were built and the population of the city’s peripheries rocketed from 591,000 in 1960 to 7.3 million in 1990, largely driven by informal growth.

Michel Rojkind and Bjarke Ingels Group’s proposed ‘New Tamayo’ cultural museum in Atizapan would have looked out over Mexico City from a steep hillside. Photograph: Rojkind Arquitectos

A 2009 project that might have addressed the dearth of services in Mexico City’s periphery was a cross-shaped annex to the prestigious Rufino Tamayo museum for the Atizapan district by Mexican architect Michel Rojkind and Denmark’s Bjarke Ingels Group. The municipality never transferred the land required for the project.

The most sweeping proposal to return Mexico City to its lake-based origins came from Futuro Desarrollo Urbano, a group of high-profile Mexican architects headed by Alberto Kalach. Their long-running Ciudad Futura proposal called for the construction of a new urban development in the area of the old lake of Texcoco. Treated wastewater was to be used to flood approximately 12,000 hectares of former lakebed. A new city would then be built on the banks of the lake with islands linked to the shore by causeways. The project was intended to kickstart the urban development of Mexico City’s impoverished eastern districts with the creation of 80km of lakefront.

Alberto Kalach’s Ciudad Futura proposal would see lakes restored to Mexico City. Photograph: Alberto Kalach

Kalach’s project hinged on financing generated by the construction of an airport but when different Mexican governments undertook to build airports in 2001 and 2015 Futuro Desarrollo Urbano’s participation was not considered. Both times the airport projects were cancelled, the first because of fierce resistance from local campesinos and the second because of a change in government, cost over-runs and environmental concerns.

The second of the projects for a new airport, proposed in 2014 by the Mexican architect Fernando Romero and the British architect Norman Foster, did actually make it to the construction phase. The plan for a vast airport in the Texcoco basin with its futuristic renders became a darling of Mexico’s business community. The project was cancelled after voters rejected it in a public referendum called by the leftwing López Obrador government when it came to office in 2018, leaving the airport 20% finished. Nothing remains of this once grand plan but a blot on the landscape.

Fernando Romero and Norman Foster’s design for a massive airport in the Texcoco basin. It was part-constructed but abandoned after a public referendum. Photograph: Foster + Partners

The grid of wide avenues called ejes has been an important source of urban blight, with traffic racing past depressed shops and disjointed housing. Another project from Romero proposed a partial solution by creatinga cultural corridor, commercial corridor and High Line-style park over Chapultepec Avenue. The 2015 proposal sparked accusations of gentrification and commercialisation, and the plans were cancelled after a referendum called by the city government.

As well as the disappearance of Mexico City’s lakes, many rivers and creeks have gone too, culverted and concreted over to reduce flooding and create space for more roads. A 2016 project by Elias Cattán of architectural bureau Taller 13 aimed to reinstate the Rio de la Piedad, which currently lies under one of the city’s main inner ring roads, Viaducto. Cattan’s plan envisioned putting the freeway in a tunnel under the river, and building a linear park on the banks of the resurrected stream.

While the Rio de la Piedad project has failed to find backing, the newly elected mayor, Claudia Sheinbaum, has recently announced her intention to start recovering some of the city’s waterways.

Follow Guardian Cities on Twitter, Facebook and Instagram to join the discussion, catch up on our best stories or sign up for our weekly newsletter