There is a possibility, but it's only in theory because, like Gold, they can't control the market. If they had their way, they would have controlled the market, but they can't because there is not only one institution that holds it. The same can be said about Bitcoin. I saw an update on Bitcoin Magazine that said public companies hold about 1 million bitcoins. The public company in question is not just one company, but hundreds of companies, so it's difficult for them to control the market because who is the actual controller going to be?

The same can be said about the question of "will government control the market". Who is going to control it? China, US, Russia, India. UK, France, Germany, Canada? Other countries are not going to sit by and let one control the market in a way that favours them alone (if that's even possible). This is why I know no one will have control over Bitcoin even if it were possible.