Arguably, they are the ones most affected with the most to lose. A salaried employee with no stock options likely depends more on their continued paycheck and the continued success of the company than any large shareholder or even the class of employees who hold stock.
Their vote should count MORE than the board.
The media, of course, isn't owned by workers, and so rampant character assassination is par for the course for anybody who moots ideas like this ("czech spy", "arch brexiteer", "anti-semite", "terrorist sympathizer", etc.).
I understand why this isn't practicable. Those who have large investments have a large incentive to educate themselves on how the market works and how corporate governance will impact overall success for the company.
Sometimes hard and unpopular decisions are necessary in order to keep the company profitable.
I do, however, see real value in having input from a sector that's focused more on long term success than short term profits.
The question is, how well can you sell it and whether the conditions are otherwise acceptable.
Your landlord, most of the time (i.e. when they're not repairing or maintaining their properties), is not trading money for time; they are charging you for access to materials which, moment to moment, costs them nothing.
Patent trolls make money without trading away their time -- you work to pay for access to an idea, which costs them nothing to maintain.
One could go on and on with examples of widespread rent-seeking fields of work and industry; but in general, no, it isn't literally everyone who trades time for money.