“There is always some controversy around large iconic buildings,” said Mike Holleman of Heery International, the architectural firm that designed the stadium for the 1996 Summer Olympics in Atlanta. “They are opportunities for countries to say to the world: ‘We’ve arrived, here’s an iconic venue. We can do that.’ That is the goal, to show the world that you can step up.”

Indeed, the Japan Sport Council, which governs the Tokyo stadium, said in an emailed statement: “We aim to build Japan’s National Stadium to boast to the world.”

Sometimes, a country appears to get it right, as China seemed to do in Beijing with its National Stadium for the 2008 Olympics — nicknamed the Bird’s Nest because of Herzog & de Meuron’s lattice exterior. It received international acclaim for what The New York Times called its “intoxicating beauty.”

The Tokyo stadium faces another challenge that has dogged its cousins: It must avoid becoming an economic burden by carving out a life as an arena long after the closing ceremonies.

Montreal’s stadium, for example, designed for the 1976 Olympics by the French architect Roger Taillibert, left the city with $1.5 billion in debt that took 30 years to repay, earning the arena a nickname change from the Big O to the Big Owe. Scheduled events there are sporadic, as they are for the stadium used for the 2004 Summer Olympic Games in Athens, which has been widely criticized for not having a post-Olympics plan. One success story is the Los Angeles Memorial Coliseum, which has twice served as an Olympics arena — in 1932 and 1984 — and continues to be used for college football and other events. Olympics officials are emphasizing permanent use in evaluating possible sites for the 2024 Summer Olympics. “The problem with Olympic stadiums is it’s somehow the most terrible commitment,” said Jacques Herzog, one of the Bird’s Nest architects. “You have to think about what will happen after the Games are over. The majority are there for nothing, or are ruins, or don’t really have a meaning anymore.”