Should work....... for awhile. Wait until the employees want to retire or quit. Will other employees buy them out? Will they still receive “dividends” if they retire. Doubt if new employees get stock.
Lots of corporations have privately traded stock that is not on any public exchange. Architecture, engineering, design and construction firms are often structured like this. The board sets the price of the stock and you sell your shares to the company when you leave. Incentives are structured when you join that specify how much equity you get.