However look at the problem using game theory and it changes. Once customers learn that they can standby for free, some of them will buy tickets on the cheap late evening flight rather than the expensive peak hour flight. That behavior change will definitely save those customers money and cost the airline money. Advocates of free standby know this and in fact it's why they advocate it, not realizing that the airlines would not be able to maintain their current pricing under a more liberal policy.
In summary, the right answer for a one-time, never to be repeated event is different than the right answer for a permanent policy decision.
You've raised a fascinating issue, that of game theory. I must do some homework. However as a first stab:
That all customers share the same objective: minimize price paid - does not mean that there is no conflict between the objectives of one customer and that of another. Customers compete with each other for not just seats, but seats at particular scheduled times - or in other words, their relationship with each other is not a simple one. As you have pointed out, should all customers universally aspire to standby for more favourable flight times at no additional charge, such behaviour flies in the face of laws of supply and demand as they apply to price. I'm struggling a bit here, but I think it has to do with a passenger generally enjoying the service he or she gets for the price he or she pays because, and not despite, his or her being but one of a group of customers. Thus, attempts to understand airline seat pricing must take into account group dynamics, as opposed to just laws or rules devised for one customer to one provider situations.
For example, in the example you gave, that of people attempting to standby for higher priced flights for no additional charge: The term 'standby' becomes meaningless, if there is nobody on the plane that ever paid the higher price, because virtually everyone interested in the flight opted to 'stand by' instead. The nature of the collective customer demand has not changed, only the time at which the customers reveal their demand (the last minute before takeoff.) .