But when a city/region/country tries to vastly increase prestige by hosting, it's often a big strain on their economy and can leave a legacy of waste.
It's one thing to use a big event to upgrade or build facilities that are in demand and will be used, but construction costs were hard to justify. But it's a waste when they're built and then not used after the games; which is unfortunately common.
You can often sneak in some infrastructure projects that will be of lasting benefit too. As I understand it, LA's network of highway information signage was built for the 1984 Olympics, and is sort of useful for other things. I read that Paris built some runoff storage/treatment facilities to augment their sewage system[1] so that they could run Olympic events in the Seine, but improving water quality will benefit residents and the environment after the games.
[1] Most old cities, including Paris, have a first to market problem with their sewage systems. When there was little concept of sewage treatment, it made sense to build combined sewers that manage rain water and sewage in the same system; you didn't want either in the streets, so pipe it all to the river. Over time, sanitary sewers required treatment plants to clean the water before discharging it into the river; but in a combined system, rain water will oftwn overwhelm the treatment plant capacity, and you get less treated or minimally treated discharges during sustained rainfall. It's difficult to build a second system in an established urban environment, but cities that grew in the 1950s or later tend to have separate storm and sanitary sewers. Of course, time has shown we should treat water from storm sewers too, when possible.