The employees may be "the ones doing the work" but capital investment is key to allowing them to do that work productively. The shareholders provide that capital, which (formally or informally—they're not obligated to provide it in the first place if they don't like the terms) means that they get to decide how it's used. The board is their agent in making these decisions. If they're smart they'll pay attention to what the employees recommend within their area of expertise—but then again "individual contributors" are often more or less ignorant of, or at least less focused on, certain aspects of running a profitable business which are nonetheless essential to remaining in business. To pick one obvious example: If your engineers create something very impressive from a technical point of view, but there isn't a large enough market willing to pay what it would cost to manufacture, then the product will fail. If that happens, the engineers are salaried employees and have already been paid for the work they put in designing the product. They may be looking for new jobs if the company goes under, but the shareholders who fronted the capital for that development hoping for a long-term payoff risk losing their entire investment.

If employees of a publicly traded company want representation on the board they can always buy shares, individually or e.g. via their union if they have one. However, not wanting to take that kind of risk is a big part of why people choose to work as employees of someone else's company rather than being self-employed in the first place. It's safer to take the regular paycheck and invest your savings in a diversified portfolio rather going all-in and investing heavily in your employer.