19 year olds can be careless when driving. All statistics prove this to be sadly, and sometimes tragically, true.
Are her roommates going to help with the costs of the communal vehicle? Rather than having free use they would benefit more from sharing the responsibility inherent in owning a vehicle and, most likely, will be more careful when using it. You could insist that being a named driver on the insurance (and paying an equal share in that and fuel and upkeep) is a prerequisite for driving. Once they understand that they’re not getting a free ride (no pun intended) and their actions may have consequences they will likely show whether their intentions are egalitarian.