The website for Rome's Anagrafe, Stato Civile, and Leva offices provides a good example into how much work Italian civil registration offices really handle a year, how much work this particular cities' 3,800,000 citizens generate.
Citta di Roma - Anagrafe, Stato Civile, Leva
Amongst the list are:
Transciption of 130,000 civil records (births, adoptions, acknowledgements disclaimers, marriages, citizenship, burial)
Managing the 8,700,000 civil records being stored in this office (1871-onward)
Managing the 70,000 (adoptions, awards, marriages, divorces, separations, etc.
Transcibing 15,000 marriage banns
Performing and transcibing 4,800 civil marriages
Issuing 500,000 ID cards
Managing the register of residents abroad (A.I.R.E.) - this is the register you are transcribed into when you get your dual citizenship.
Managing the population database
Digitization of records for non-centralized access
...and it goes on.
This is why they often don't have time to do extensive research for you. I used Rome as an example because their website is so descriptive but the concept applies no matter what civil office you need to contact in Italy. Your genealogical requests need to be clear, concise, and not require them to do a lot of research. Many offices, especially those in large cities like Rome, simply do not have the time to do more then is specifically asked for.
So, I would suggest researching in U.S. records first to get as close to the true information as possible before sending letters to Italy. Then make them as clear as possible and include all the information they need to locate the record for you quickly. If you do this, your success rate will be much higher!