As I understand it, this only has to be done when accessing your Apple ID from a new device.
Yeah the old system was a real pain to use. This one is much better, it just asks you to pick a device to get a code from, it'll pop up and you type the 4 digit code in.
You are describing apple's old (although still working if you have it enabled) 2 Step Verification.
The new 2 Factor Verification doesn't require you to pick a device, and it doesn't use 4 digit codes.