Why you can’t find records on microfilm for Rome.
Ancestry has partnered with the Mormons to include many Italian records.
When the Mormons did their filming in Italy they negotiated with the State Archives. Most, but not all, cooperated. Rome was one who did not permit filming. Salerno was another.
You also need to understand that the civil records kept in most parts of Southern Italy began in 1809 but the Former Vatican States (Rome and surrounding area and many parts of Tuscany) stopped keeping civil records when Napoleon was defeated in 1815 and reverted to the old way of having the church keep track of the population.
The Vatican and other Church Dioceses did not permit filming either.
To get records back to about 1871 you can write to the individual town or city and request them. Before 1871 you can write to the Vicario di Roma but you will need to know which parish they belonged to.