The entire idea of the free market is that, once externalities are internalized and the market is properly governed, the best way for a corporation to improve society as a whole is to increase its own profits. It turns out that improving society as a whole is a vaguely defined and difficult goal, while increasing profits is directly measurable. The market works by taking something vague and difficult for anyone to set out to do on their own (improve the well-being of society) and turning it into a direct, self-interested, measurable goal (increasing profit).
There are other systems that work a similar way. For instance, the adversarial system in criminal justice works by throwing together two opposing lawyers, each of whom wants only to win the case, and as a result does a pretty decent job of both enforcing the law and protecting civil rights.
You're absolutely right about how that should work in theory.
once externalities are internalized and the market is properly governed
If a company chasing down profits hurts the general public it is a failure of the market, not the company. However, for this to work in practice, there needs to be a strong firewall between the companies competing, the regulators defining the market and even the media informing the public about what is going on.
We're watching a rigged game where the coaches have paid off the referees and the sports reporters have realized there's more money in becoming promoters.
So the market only partially works. Perfection is an unattainable goal. Fine.
As you run a business, it should be pretty obvious to you whether you're profiting by exploiting flaws in the system. If you're not exploiting flaws in the system and you're still profiting, I don't think you need to worry a great deal about whether you're actually benefiting society. Most businesses do a small, dull, unexciting part of benefiting society, and that's fine.
once externalities are internalized and the market is properly governed
That is the problem though, we are nowhere near the point where externalities are internalized or markets are properly governed. Presently any externality which can be ignored is ignored in the interests of maximizing shareholder value. This becomes doubly true when a company is really feeling the squeeze from the market. Every industry and business has externalities which are not being paid for at the moment. One is the environmental costs of manufacturing, infrastructure and energy. Another is dealing with repressive regimes. These are costs to society.
Regulation and enforcement are always met with market hostility because someone has to pay the cost (and whoever is paying usually doesn't want to). Self-regulation rarely works, honest companies may play by the rules for a while but eventually someone will decide they can make more money working around the rules.
Free market ideals are great and they all work on paper. I think it's a fine goal but an unlikely reality. Here in the present we are not moving towards a free market. Most moves to open markets are not making them freer they are merely giving greater power to the entrenched players. Until the market is truly free there is real damage being done to people and the planet.
There are other systems that work a similar way. For instance, the adversarial system in criminal justice works by throwing together two opposing lawyers, each of whom wants only to win the case, and as a result does a pretty decent job of both enforcing the law and protecting civil rights.