So what’s the easiest way to unlock an iPhone after it has been released for use on another carrier?

Is it, as most will tell you – Apple included, to completely restore the phone through iTunes?

No. Simply insert a SIM card from another carrier and wait for a minute or two (use common sense with any prompts that may appear).
Note: carriers tell me that the unlock can take from 1 hour to two days, so if it doesn’t work it’s worth waiting a couple of hours and trying again.

As always, ensure you have backed up your iPhone first.