I put my iPhone down, screen-down, quite often.
(I do use a case that has a lip that protrudes beyond the level of the screen, protecting it.)
There are a couple of scenarios where I do this:
to stop push notifications on the lock screen distracting me when I'm at work.
it discourages others from reading incoming messages, emails etc when I place my iPhone on a shared table (eg at a social event)
I know both can be deactivated from the lock screen, but their benefits at all other times outweigh the need to do this for these situations.
Also, placing your iPhone face down allows you to be polite when with company, not letting your phone take priority over a face-to-face conversation. You can discreetly turn it over to check it when appropriate.
Fair enough, but if a case is being used it would presumably stop the phone from wobbling because of a convex button.
Also, if you want to be polite, why even have your phone out of your pocket?