A majority of the shares in most publicly traded corporations are held by retirement funds, both "private" (BlackRock, Vanguard, State Street) and public (FERS, CalPERS, ...). These entities, generally, have no appreciable interest other than maximizing profit. They are all regulated financial entities, even the private ones are quasi-governmental (e.g., BlackRock has close business relationships with the Federal Reserve), and the public ones are just straight up government agencies.
So, in a pretty real way, there is a legal requirement, though like many such things in the United States today, it is not properly formalized.
But then you have to make a different statement. The purpose of a large, publicly traded for-profit corporation is to maximize profit.
This is quite an important distinction because it implies we may want to limit the prevalence of those things and increase the prevalence of small businesses and privately-held medium businesses that can advance other societal goals.
It is not clear to me that large and/or publicly traded corporations must maximize short-term profit. The seminal case of shareholders vs management concerning the Ford Motor Company in its early days shows that the objectives and incentives are not beyond debate and thus not intrinsically tied to the size or ownership model of a company.
The government has consolidated around the current set of incentives, both directly through its own arms and indirectly through legislation and policy, leading to the result we see today. Breaking these large businesses up may lead to some disruption for awhile, but if the incentives stay the same, the same end result will likely be arrived at again before too long.
So, in a pretty real way, there is a legal requirement, though like many such things in the United States today, it is not properly formalized.