Management has to act in shareholders' best interest. Management decisions cannot be self-serving at the expense of shareholders. Shareholders are a diverse bunch and can be interested in things besides pure profit, and companies can choose to maximize on those alternative dimensions.

The Supreme Court said as recently as 2016: "Modern corporate law does not require for-profit corporations to pursue profit at the expense of everything else, and many do not."[1]

From that same article, there's more:

"More to the point, corporate directors are protected from most interference when it comes to running their business by a doctrine known as the business judgment rule. It says, in brief, that so long as a board of directors is not tainted by personal conflicts of interest and makes a reasonable effort to stay informed, courts will not second-guess the board’s decisions about what is best for the company — even when those decisions predictably reduce profits or share price."

1. https://www.nytimes.com/roomfordebate/2015/04/16/what-are-co...

"While it is certainly true that a central objective of for-profit corporations is to make money, modern corporate law does not require for-profit corporations to pursue profit at the expense of everything else, and many do not do so."[1]

Public or not, people involved in a business do have fiduciary duties to their investors. But those duties are not specifically about profits. They are about "obedience, information, loyalty, and care"[2].

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[1] https://caselaw.findlaw.com/court/us-supreme-court/13-354.ht...

[2] https://online.hbs.edu/blog/post/fiduciary-duty-to-investors