Quick Start is not available on iPhone/iPad

The profile item that controls Quick Start is
Allow setting up new nearby devices (supervised only, iOS 11.0+) in the Restrictions payload.
If it is set to OFF, change it to ON and try again (the default value is ON).

This setting applies to the source device of Quick Start.
Quick Start can be used on a device in its factory-default state even without an internet connection, so the new device is not affected by MDM settings.