Only those who could afford to pay the state for the license to connect private pipes to public aqueducts could have a private water supply. The license wasn't especially expensive, but it was certainly a luxury--the city was filled with public fountains, so there was little need for a private water supply for anyone but the extravagantly wealthy. As regards to wealth, your assumption that only the patricians had wealth is entirely untrue, particularly by the time of Augustus, when the license to connect private pipes began to be sold--see here. Plebeians could be just as wealthy and often were vastly wealthier--the equestrians could not exist if the plebs could not gain extraordinary wealth. The social orders are a political distinction, not an economic one, and they're a social distinction that began to lose importance as early as the 5th or 4th Centuries, B.C. and were almost totally irrelevant by the end of the 3rd