I understand exactly where you are coming from as I wondered this too!
The interface gives the impression that you should click snaps, then select ‘Face’ as the target, and then below it lets you select ‘Center’. Now if you can’t snap to a face center, that should be grayed out, or give a warning, but it just silently fails. Yes you can snap to the face, but not to the center, just anywhere on the face’s surface. Very misleading on Blender’s part unfortunately. Another example of implicit program functionality where you are not told it cant happen, because it’s assumed you know this somehow, or, buried somewhere in the docs and assumes you read said doc page.