So first off, TOTP and similar already solve the "phone is present but offline" issue.

But even if it didn't - how on earth is this meant to work? I'm somewhere that has no cell service, not connected to wifi, and need to login to something on a public computer..

Ok so with TOTP I just get the 6 digit code my phone generated, and type it into the input on the public computer, the site confirms its the expected OTP and I'm in.

How does this work with a QR code? The phone generates a QR code... How does that help me login on the other device? You're assuming the other device will (a) have a webcam and (b) have reasonably easy access to capture an image via it and upload it via the browser...