Answer
If you are only travelling around the peninsula, a car is not essential: you can get between central streets, the port, and nearby beaches on foot, by bus, or by taxi. A car becomes noticeably more useful if your accommodation is far from the center or you plan to visit Casapueblo, Piriapolis, remote beaches, and several stops in one day.
The decision depends on the season and the makeup of the group. In summer, parking in popular places is more difficult, and public transport may run less frequently in the off-season. For families with children, luggage, or limited mobility, renting a car usually saves time, but insurance, fuel, tolls, and parking must be added to the rental cost.
Before booking, make an itinerary for each day and check the bus stops near your accommodation. If a car is needed for only one trip out of town, renting one for a day or taking a taxi may be more cost-effective than having a car for the whole holiday.