The model she proposed -- 40% of directors representing labor, not shareholders -- is similar to what's used in Germany, where boards of directors are 50 / 50 split between labor and shareholder representatives. Germany's doing fine under that system. They're the 4th largest economy in the world are are plenty capitalist, with companies like Adidas, Puma, DHL, Bayer, Volkswagen, BMW, Mercedes-Benz, SAP, Allianz, and Bosch. If it comes to pass, I wouldn't worry about the foundations of our economy.
That said, the reason shareholder value theory is so dominant in the US is because it makes equity capital cheaper and more efficient. Providers of equity capital will demand a higher return if they don't have assurances that directors will be looking out for their interests. There are many situations when stakeholder interests are in direct conflict. As an employee, for example, I want to be paid a lot more money. I don't expect the board of directors to represent that interest. If a director makes a terrible decision and loses shareholder money they could simply say 'oh but it helped bondholders/employees/the community' and it's a lot harder to hold them accountable.
This bill has no chance of passing in this Congress, so it's more of a display of Warren's idealism than a pragmatic law. A lot of the ideas proposed would have significant unintended consequences that I would expect to be ironed out in a final bill. For example if you require longer holding periods for stock, CEOs will just demand more cash compensation to make up for it. If you discourage stock buybacks (a silly idea), companies will just pay more dividends. And if you discourage both they'll just sit on cash and be more likely to waste it on vanity projects. They're never going to pay employees more than the market rate by choice.
I think its telling that the most vocal advocates against the 'shareholder capitalism' approach are actually large corporations and their executives themselves, which is why it's striking to see Warren pick up this mantle. Strange bedfellows. If you erode shareholder accountability by requiring them to represent diverse, often-conflicting interests, you remove pressure and a key mechanism from executives to follow through and act responsibly with other people's money.