Wow, I always had the impression the red flag is set by the mail carrier to indicate for the house owner (particularly in rural areas) that new mail is inside the box. (Hence it would save the owner a trip for checking.)

But this way around it makes a lot more sense.

Some mailboxes have an indicator that mail has arrived, but they aren't the norm. The indicator is raised by the action of opening the door, so the mail carrier doesn't have to do anything. It is on the person getting the mail to reset the indicator. This indicator is separate from the flag that signals the carrier that there is mail to pick up.

Tbh, as long as you make the mail obviously not placed by them they'll take it. (as in don't need to use a flag).

Like they always shove (or drop) it into the mailbox so when there's letters that are obstructing the box from closing properly they know they didn't place them there so it's outgoing and they grab it.