The news came as organisers scramble to deal with teething problems including accommodation issues and an outcry over the fate of stray animals being rounded up in Sochi.
Double Olympic champion White, one of the biggest drawcards of Russia's first winter Olympics and among the world's best known winter sports athletes, said on Wednesday he did not want to risk his chances of winning a third halfpipe gold medal.
White's decision came after Norwegian Torstein Horgmo, another medal contender and triple X Games gold medallist, broke his collarbone in a crash on the course on Monday and was ruled out of the Games.
The course was then modified but the changes did not go far enough to keep White in the competition.
The American, who hurt his wrist on Tuesday after falling on a course he described as "intimidating", said it was not worth the risk.
"With the practice runs I have taken, even after course modifications and watching fellow athletes get hurt, the potential risk of injury is a bit too much for me to gamble my other Olympics goals on," White told NBC.
With the focus set to shift to sports on Friday, the International Olympic Committee cast its eyes past the most expensive Games ever staged to look for ways of revamping the global sporting spectacular.
Russian President Vladimir Putin has staked his personal and political prestige on hosting a successful Games and turning the Black Sea resort into a more attractive tourism destination.
Ratings agency Moody's said in a report on Wednesday that the Sochi Games, which have cost a reported $50 billion, were unlikely to provide much of a boost to the Russian economy.
The IOC, who picked Sochi in 2007 despite it having virtually no venues in place, said it was time to take another look at the cost, size and bidding process for the Games.
Several cities have already pulled out of the race to host the 2022 Winter Games amid concerns about rising costs.
Protests in Brazil ahead of this year's World Cup and the 2016 Rio Olympics have further highlighted the problems associated with hosting mega sports events.
"We believe we should do more to support better bid cities in their engagement," IOC Vice President John Coates said at the start of the IOC session on Wednesday.
"Are we not asking too much too soon (from bid cities) Should the bidding procedure be more an invitation of potential bidders rather than a tender for a franchise The cost of the bids concerns us all," the Australian said.
The discussions, part of the IOC's Olympic Agenda 2020 launched by President Thomas Bach, comes as athletes arrive en masse at the Black Sea resort.
Security remains a top priority for Games organisers with the Olympics a target for Islamic militants as U.S navy vessels entered the Black Sea for routine security operations this week.
The USS Mount Whitney, the flagship for the Europe-headquartered U.S. Sixth Fleet, moved into the Black Sea on Tuesday and the frigate USS Taylor was arriving in the waterway on Wednesday, U.S. defense officials said.
"They're there to conduct routine security operations and patrols," said Army Colonel Steve Warren, a Pentagon spokesman.
"I think we've made it clear previously that having them positioned in the Black Sea during the Sochi Olympics gives us an added capability in the region."
Washington has it would have two ships in the Black Sea in case Russia needed their help. Moscow so far has not made a formal request for assistance from the ships.
For one new Olympic event, friendship will outlast the competition.
American slopestyle snowboarder Sage Kostenburg told Reuters he hoped the sense of friendship with his fellow competitors would not melt away when qualifying begins on Thursday in the new event aimed at attracting a younger audience.
"I really hope not, we're all pretty good friends and we get on well, so it would be a shame if all that was to change and everyone turned up tomorrow all serious," the 20-year-old said, grinning.
"Obviously I would be so stoked to win an Olympic medal, but just the fact that slopestyle is in the Olympics for the first time is so sick. Not many people get to do this, you know"
For some snowboarders, however, the focus is still on the controversial course.
"The big jumps are very big, especially for the girls," Russia's Sarka Pancochova told reporters after Wednesday's practice runs.
"We are very little, we have 30 kilograms difference to the guys. It's hard to get the speed you need. It's just a game, we have to figure it out."