> Being able to buy and sell shares is not problematic per se, but there should be rules in place that give all workers of a publicly traded company better access to owning parts of said company.

Thats not a bad idea. If it was required to run some sufficient percentage of the company as if it was a cooperative and give a defined amount of shares to any joining employee for X years of service and also give representation to the workers in the governance of the company, things could be better. Europe already has the latter in the form of 'work councils'.