Try to start a democratic company (or run a thought experiment about doing so) and you will probably find the reasons why democracy works better as a way to manage a society than a single company.
It does happen. Both the largest supermarket chains in Switzerland are cooperatives.
However, small competing firms in a market where people vote with their wallets is already pretty democratic. The voting takes place at a different level - people choose companies rather than leaders or direct policies, but it works well enough.
There are worker cooperatives: https://en.wikipedia.org/wiki/Worker_cooperative
Workers' self management: https://en.wikipedia.org/wiki/Workers%27_self-management
And serious economists who advocate for such a system: https://en.wikipedia.org/wiki/Branko_Horvat