As an Italian citizen who mostly lives in San Francisco, I have to carry my Italian ID card while traveling in Italy. I went to renew it last year in the ancestral town a three hour drive in the hills outside of Naples. When I arrived, they said they couldn't do it because the person wasn't in. I went outside and found her having a pizza, and brought her in. She started up the computer and looked me up. It had me living in El Paso, Texas. I told her I went to college in El Paso and left in 1978, moved several times since then, and have lived in California for the last few years, and that I have always informed the Italian Consulate when I move.
Not to sidetrack the thread, but you don't need a carta d'identità, as far as I know. You can carry your passport as identification instead. It's just bigger and doesn't fit in your wallet
If you were issued a carta d'identità, the consulate can renew it for you if you're AIRE registered when it expires - meaning they can't issue you the first card, but they can renew it.
Just curious, are you getting your comune to issue you the plastic chipped carta d'identità, or are you getting the paper version since (I presume) you aren't a permanent resident in the town?
(Note: I could be wrong, but that is my understanding regarding ID. And bigger picture as you pointed out with the bureaucracy, you'll get different answers depending on who you ask)