You'd save the QR code at the time you first used it on the old phone, and not wait for when you needed to transfer it.
For me, I'd usually be on the desktop when setting up 2FA anyway, so I'd just save the QR code from the desktop browser ("Save image as ..."). When I needed to set up a new phone, I'd open the saved image on the desktop and point my phone at the screen.
That's an absurd expectation. First of all, many users don't even have or use a computer. Of course, I personally do have one, but I'm often nowhere near one when I set up MFA on a new account. So then I guess I screenshot the QR code to my phone? But if I saved the image to my phone it gets stored in my photos backup anyway. Why would Authenticator not just back its own contents up, to that exact same spot, rather than me doing some crazy runaround that for some reason involves images?
For me, I'd usually be on the desktop when setting up 2FA anyway, so I'd just save the QR code from the desktop browser ("Save image as ..."). When I needed to set up a new phone, I'd open the saved image on the desktop and point my phone at the screen.