Companies give the olympic games funds for their advertising in and around the ground, and on television. Without these funds, the olympics would likely have a significantly reduced budget, meaning that the games might have lower quality equipment. As the games are the height of competition in many sports, they should be allowed to raise funds by any means necessary to provide the proper equipment for athletes.
I believe that US should be allowed to profit from the olympics. In our capitalistic society, companies have the freedom to advertise and market their products however they desire. Since the Olympics is a demonstration of pride in our country's athletics and is watched in millions of homes across the country, it is smart for companies to try and capitalize this event. Companies can sponsor other sporting events and often, companies sponsor individual celebrities and athletes; thus, they should be able to gain profit off of the olympic games, much like they would off of other sporting events.
There are no laws that say companies cannot profit from the Olympics. The Olympics is not some type of public games where only the government can decide what they can do. However, with the track record lately of the Olympic committee picking not so great places to hold the games as well as the games' effect on local economies and everything I'd probably say there might be a problem with supporting them in the future.
The US should not be making bank on an organization it is not taking the bill for. Rio, on the other hand, is in dire need of financial aid. The very least thing we can do as a global collective is allow Rio to get the profits from these games and spend it rebuilding their very, very broken infrastructure.