What is the value of iCloud.com if 2FA requires your device?
The first time you access a 2FA-protected iCloud account on any device you've chosen to use with 2FA, you must provide the correct credentials with that device to assure iCloud that it is indeed the device you've selected to receive 2FA authentication. You are then offered the choice of ignoring future requests for authentication on that device for some duration of time. Every so often, you must re-authenticate with the 2FA credentials to reassert your identity. Does this help?