No, that's not normal (asking for my ID or address).
In fact, I created a new battle.net account. Located in Singapore. No address or government ID needed, I just curse the people at Blizzard everytime I have to log out of the SG account to play a game that is linked to my original (DE) account.
So they believe me, without verification or anything, when I create an account in Singapore. They consider me a liar and hold my account hostage before I provide details that I'm not willing to share when I tell them that my existing account should follow me.
That is _not_ normal. That's bizarre and stupid. If they'd require this for every account, new or changed, then it would be consistent (but .. I still would think that's not okay and wouldn't create an account with them). Handling these cases differently is just hurting the existing account in good standing.
(for the record: I don't have any utility bill, electricity or otherwise. That policy is not only brain dead, it wouldn't even work for me if I wanted to hand over anything like that. Singapore: My utilities are covered by my rent, I don't get bills for that. I don't get any physical bills anyway and literally the only bill I have would be an online mobile bill. Coming from Germany: I get a utility bill (water, electricity) once a year. This whole idea of proving my address is not only utterly stupid, it also seems to expect things to work in ways they don't outside of Blizzard's home country)