There are a couple of apps I use that don't have Mac apps and whose websites are particularly clunky and always require a 2 factor code (my previous company's timesheet service is a prime example). It was way faster for me to use mirroring to enter my time than log in, complete the captcha, wait for a two factor code to come in, then have to log in again.
But my phone also lives in my pocket while I'm at my desk, so that may influence things. If your phone is already sitting on a dock or something I can see why it’d be less useful.
So, if I understood correctly, that feature exists so that, for example in your case, you wouldn’t need to take your phone out of your pocket? 😮