The actual monetary cost to the airline of putting you on a different flight, later or earlier is, let's just say not really a factor.
This is more a case of revenue management or enhancement over anything else.
Because the value of the earlier flight is higher to the customer than the airline, the airline has determined, correctly, that passengers are willing to pay for the privilege. If the customer is willing to pay, no reason to leave that money on the table.
It also serves as form of price protection. If the earlier, or later, flight is generally more desirable, the ticket price will be higher. They don't want passengers paying for the lower fare flight, then taking the higher fare flight without paying something for that privilege. Otherwise, it's lost revenue.
Waiving those fees for frequent travelers is a benefit designed to keep you flying with them. The 'lost' revenue for that benefit is more than recouped through additional ticket purchases.
A prominent outlier in the Standby model is Southwest. But, that has more to do with them having no change fee. They will happily change your flight to anything you want, you just pay the difference. Essentially, they don't have traditional Standby at all. For clarity, they do offer fare protection in a 2 hour windows for A-List members.
Finally, staff do have some flexibility to waive any fees if there's operational justification for doing so. If flight B is significantly delayed, pax can be moved to flight A. Yes, this is mutually beneficial since the passenger is underway sooner and downstream effects, missed connections etc, are mitigated.