Of course, since many companies prefer less regulation, the last thing they'd want to do is hand over the keys to what they do for the healthcare for their employees over to the government. With things how they are now, they can always cut or pair back their plans if they want to cut costs. That lever would be gone with single payer.
Like many things, the system is set up to benefit those in charge rather than those who it's meant to serve. You can look just about anywhere outside the US and see that universal healthcare is a much better system, but better for who? Not much of a benefit for those who make the decisions, so we keep the flawed system we have.