No, that is very uncommon. Rome is a safe city. Pickpockets think they are just taking something from a careless person. To them, seeing a wallet or a phone in an open purse, or sticking out of someone's back pocket is like seeing it lying on the floor. They just pick it up. It's sneaky crime. There is very little confrontational crime where someone does something physical to you like grab, snatch, pull something, or threaten you. Yes, it can happen, but is less likely to happen in Rome than most other major cities. It's much less likely than in London or Paris, for example.

At night around Termini there is the occasional purse snatcher, where there is aggression, which is different from pick pocketing. it happens. Just take the usual precautions, especially on the train or bus.