And why do we always have to be "online" even when not doing anything multiplayer-related? Why doesn't Blizzard (or others such as Steam) explain that to us?
Ah, the good ol' days of true offline independence...
It's rather simple (and Valve have explained in the past);
Load Steam up.
It automatically creates a digital thumbprint.
You can then play offline.
Change hardware, want to buy something new, want to play online - connect to the internet and go online.
It's not a problem at all. It doesn't even need a fast connection to create a thumbprint. You can log on using a mobile data connection for a second and you're done.
Lastly if an internet connection is important and you don't have one where you live, you should probably look into moving or live in a place of such poverty that games should be the last thing you need to worry about.