You don’t need to own a car in Placencia, but you probably would want to. You can get around with a bicycle, some people have golf carts, and a very few people have scooters, but that is an option.
The reason that you might want a car is because Placencia is such a small village, and though there are some 4 or 5 grocery stores, 3 banks for ATM, and hardware stores, your daily needs are met. However, you know if you're in such a small village, you're on a peninsula that's only at that point of the village less than a quarter mile wide. You might want to get out sometimes just to do something different or see a different view. To do so, you just have to drive along the only road along the whole peninsula for about 20 some miles. The peninsula itself is only about 18 miles and then you start going inland a little bit, but you're still just on one road until you get to another highway, which is about 24 miles away. So just to get a little a bit different experience, a car would probably something that you would want to do.
There is the Hokey Pokey water taxi that takes you across the lagoon to another village, called Independence, that costs US $5. When you get to Independence, there are some more things to do and see. But there aren't things like movie theaters and there aren't shopping centers. There's no such thing as a fast food restaurant, so while you have everything you need in Placencia, for me personally, I would get a little bit tired of just looking at the same thing day in and day out.