For centuries Parisians have emptied sewage into the scenic River Seine, rendering it unsafe for swimming. A $1.5 billion clean-up in advance of the 2024 Olympics was supposed to fix the problem. But, with the Games now over, the river was safe for swimming only some of the time. Last week, four athletes — two from New Zealand, one from Belgium and another from Switzerland — acquired gastrointestinal illnesses after competing in its waters.

Parisians footing the bill are understandably frustrated at the colossal expense and unfulfilled promise. Amid an Olympics promoted as the greenest ever, it looks — and perhaps smells — like textbook greenwashing.

But is that such a bad thing? From Beijing’s temporary air pollution clean-up in 2008, to the partially laundered Seine in 2024, Olympic environmental megaprojects nearly always fall short. Yet even when they do, they still improve the environment in some way, and provide a positive example for future Games and cities.

The modern Olympic Games have often served as a convenient excuse to build expensive, environmentally destructive infrastructure. Stadiums and other sporting venues are the most obvious examples, but everything from highways to athletes’ villages are just as common. After the celebrations are over, the new construction is often underused and even abandoned. This has been an ongoing and embarrassing problem that has grown with the expanding scope and expense of the Games.

Then in 1988 things started to change. That is when the small town of Lillehammer, Norway, won the right to host the 1994 Winter Olympics, and — spurred by environmental activists — quickly embraced the idea of making them sustainable. For example, facilities were built for energy efficiency and with an eye to post-Olympics use. These were modest efforts by today’s standards, but in retrospect that year’s competition shifted how hosting duties were won, and are today widely regarded as the first “green” Games.

By the early 2000s, aspiring host cities realised that snagging the bid required a public commitment to a more sustainable mega-event with a tangible environmental legacy.

Enter Beijing. As far back the mid-1980s, the Chinese Government publicly aspired to host the Olympics. However, it was not an easy sell. Among other issues, Beijing had some of the world’s worst air pollution. So, to win the rights to the 2008 Summer Games, China promised an ambitious $12 billion clean-up of the city’s smoggy air that included factory closures and relocations, shifts to cleaner burning fuels and traffic restrictions.

The strategy worked during the Games. Pollution plummeted and skies that had been grey and hazy for a generation were suddenly clear and blue. But afterwards, the temporary nature of many initiatives was revealed when the pollution returned. Was it an egregious example of greenwashing? Yes. Yet it turned out to be something more than that, too.

In Shanghai, where I lived in the years before and after the Olympics, the winter haze was accompanied by online and in-person grumbling about whether the Government was actually capable of meaningfully addressing the pollution even if it wanted to. The Games, citizens reminded each other, proved that the haze could be cleared if the will existed to do so. By the early 2010s, there was intense grassroots political pressure on the Government to fix the problem permanently.

China, through its Olympics initiatives, had acquired knowledge and policies to do just that. In 2013, five years after the Olympic flame went out in Beijing, a nationwide clean-air plan that adopted and adapted many of the techniques used for Beijing 2008 was announced. Today, China’s air is far cleaner than it was in 2008 — although far from perfect. Beijing, in turn, now serves as an example to other emerging market cities struggling with air pollution.

Perhaps Beijing might have addressed these issues eventually without the need to impress the International Olympic Committee and a global television audience. Without them, however, it would have taken much longer.

It is a pattern that other recent games have repeated. In 2016, Rio promised massive upgrades in transit and clean water that have only been partly met. But had there been no Olympics, the benchmarks would not have even been set at all. Today, some of the water is cleaner, there are new transit lines and — most important — the public expect better.

Now it’s Paris’s turn. The desire to turn the sewage-choked Seine into a swimmable waterway dates back to 1990, but it was not until the city was awarded the Olympics that there was sufficient political and financial backing to make it happen.

Still, despite more than $1 billion in spending, success has only been partial. Heavy rains can overwhelm the new system, rendering it unsafe for swimming — much less triathlons — and athletes have made high-profile complaints about what still floats in the water.

Nonetheless, that the Seine is safe even part of the time is a vast improvement that benefits Paris and its environment long after the games are over. Better yet, Parisians are unlikely to let the Government simply stop working at improving the Seine once the world turns to other host cities. Expectations have been raised; Paris must follow through.

That is not a bad outcome for a mega-project that never would have happened if the world’s biggest sporting event didn’t give Paris its blessing. Future host cities, faced with the need to create a sustainable legacy, may need to engage in a bit of greenwashing, too — and environmental activists will need to accept that something is better than nothing at all.

• Adam Minter is a Bloomberg Opinion columnist covering the business of sport. He is the author, most recently, of Secondhand: Travels in the New Global Garage Sale