Then yes, we damn well better demand that profit be the correct goal for every action regardless of organizational structure.
If our system is distorted to inaccurately measure profit locally, without properly accounting for negative externalities, then that's a legitimate problem, but the way to solve it is by factoring those hidden costs back into the profit calculation, not giving up on "profitability" properly defined.
> ... government can have another motive be primary
> rather than profit, i.e. help it citizens as the
> primary goal.
Profits are still required for gov't spending, but they are just made by someone else in the country and transferred to the gov't via taxation. Even deficit spending is just the choice to spend money today that will be obtained from taxation at a later date.
Corporations do not have any sort of exclusive lock on cost-benefit analysis.
Edit: including bad cost-benefit analysis.
In this situation it doesn't matter that yahoo is a private corporation - the same cost/benefit analysis essentially needs to be done no matter what the structure of the organization. Let's pretend that email had been created by a government agency and that agency has to decide how much of the budget to spend on security. If it costs X dollars to make something 90% secure, 10X for 95% secure and 10,000X for 99.9999% secure, etc etc eventually you have to choose how much to spend - resources aren't infinite for that government agency either. (And to make it much more difficult, they just have a guess that X dollars will make their product N% secure.) It isn't as black and white as you are trying to portray it.
I think it is fair to criticize yahoo for how the prioritized security but the same kind of issue has happened with non-profit companies and with government organizations, so no, it isn't just a "big, bad, greedy corporate problem."