One company that fascinates me is the John Lewis Partnership - this is a large (~40K employees, ~£3.5B turnover) upscale retailer in the UK that manages to be both rather successful while being an employee owned "partnership" that appears to allow employees a reasonable say in the running of the company while still have a strong management team.
They even have an explicit constitution:
"The Constitution states that 'the happiness of its members' is the Partnership's ultimate purpose, recognising that such happiness depends on having a satisfying job in a successful business. It establishes a system of 'rights and responsibilities', which places on all Partners the obligation to work for the improvement of our business in the knowledge that we share the rewards of success."
Yes. Employee-owned companies and cooperatives can be run as direct democracies.
In practice, management is a sufficiently specific and tedious job that it gets delegated. Indeed the concept of share ownership creates such a division by default.
