You really don't have to for the first couple of centuries of the Empire. The first century especially is extremely well documented until the end of the civil war in 69. It also has any number of colourful characters and political intrigue they could work with.
In fact, why nobody's made a movie or show about the civil war yet is beyond me.
I guess but the hook of the show was that you had the intermingling of the plebes and nobles, plus showing regular roman daily life.
Hmm that's more information about the people they were based on than I thought existed.