Restoring a failed external hard drive using Time Machine if drive ID doesn’t match

Time Machine can be used to restore a computer or setup a new machine from a backup. So that's awesome. And individual files too. Also awesome. BUT - Time Machine seems to fall short of being able to restore a failed external hard drive. Let's say we have several gigs of media on an external drive. We accidentally delete a file. No worries Time Machine can restore it. But if the entire drive fails. Well...then we're stuck. Hypothetically if a new external hard drive were named the same as the original in order to use as a fresh clean restoration point, Time Machine won't do it. I've been told it's not the name of the drive that matters versus its unique identifier behind the scenes. So if Time Machine doesn't find that address, then it simply thinks the drive is MIA completely. Now I could be wrong/misinformed. Does someone have a way of restoring a complete external hard drive failure using Time Machine? I hope so! Thank you.

[Re-Titled by Moderator]

Original Title: Time Machine & External Hard Drives