If all the insurance companies decide they won't insure you, how will you get health care? The government had to intervene (with the ACA) because that particular problem was so bad.
People trying to immigrate often have to use email to communicate with government agencies. If gmail bans their account, they can no longer talk to the immigration agency. I've seen a couple different people have this exact problem.
There are plenty of other examples.
Certainly governments have the power to do all these things as well, but large influential companies can absolutely ruin your life if you get the wrong kind of attention (or in the case of automated policy decisions, get unlucky).
And regardless - no business is going to send you to prison, while the state can. No business will shoot you, while the state can. So even in this interpretation of "how much can they fuck up my life" the state wins.
Businesses are free to shoot you as well, private security guards can carry guns in most parts of the US. Businesses can also send you to prison via false police reports, which is a thing that has happened periodically.