Since I might have made someone mad... to clarify, as I understand it, Bluetooth is absolutely required for this "Scan the QR code" flow to work. However, it's also possible the actual authentication traffic to travel over a different pathway (wifi, cellular), but the bluetooth part is always required though to prove proximity. So on e.g. a library computer without Bluetooth enabled, you would not be able to log in with a passkey on your phone.
Right - you can treat the protocol as having:
1. Initiation (QR code, NFC in draft)
2. (Proximal) negotiation (BLE key exchange)
3. Communication (over websockets or a direct L2CAP channel)
The challenge is that a devices without bluetooth (at least today) don't have another common way to wirelessly judge proximity. A desktop/laptop without bluetooth likely either doesn't have NFC, or has bluetooth disabled by policy and would likely have cross-device passkeys disabled by policy as well.