They could be a C corp (could also be an S corp but that comes with a 100 share holder limit), but then they have a duty to maximize profit to the shareholders. In a private corporation, the shareholders may be less inclined to sue, but the option is still there and as such the CEO must work to ensure the company is profitable. If they decide to share all profits with the employees, and the employees are majority shareholders, then this likely falls within the sphere of maximize profits.
There are things like a publicly-traded LLP which allows employees to own a portion of the company while offloading tax liabilities to the shareholder, but that is usually limited to companies which depend on depleting natural resources (think oil, gas, coal, lithium, etc)
You can have provisions about tax liabilities, but that is a specific risk that must be mitigated in an LLC that a corporation does not have to deal with, thus it’s an added risk