> They are not going to offer it to you, normally, because they are not a charity. They want to give you the least amount of money that you will except.
An alternative perspective from my time managing: That reflects the viewpoint of the business, not necessarily the viewpoint of the manager.
Getting an out-of-band raise approved triggers entire internal processes, outside of the control of the immediate manager requesting it.
Triggering one proactively as a manager with no impetus other than "this person deserves it" is likely to get denied or a token amount approved. As you said, the business wants to pay the least amount of money an employee is willing to accept. If the employee has given no indication they have issue with their current pay, the business has no reason to presume there's a need to pay them more.
However, once someone asked for one, I could take that and use it as leverage. If the employee has brought it up, there's evidence of doubt on whether the company is still meeting that minimum threshold. Denying the raise outright increases the risk of attrition, so the business takes it seriously compared to the proactive request from the manager. Then I can use what I know to work the system in the way that results in a far more favorable raise.