They don't have a responsibility to the employees, but from what I understand having all your staff walk out is generally seen as bad for business.

They have a responsibility to their owners to pay enough to be successful - but the thresholds for "mass company-ending resignations" vs "complaining on the internet" are very far apart.

This is correct. The most "obligation" that an employer might have is to pay the employee for the value of their work, and even that's dubious. (show me the source for your moral argument) They certainly have no obligation to match CoL.

If an employer doesn't pay their employees enough, those employees should leave, their employer will eventually die, and that'll add another data point to tell the shareholders to either elect CEOs that will pay more or to stop backing companies in high-CoL areas.