Saving the cost of a rental car and just using free Disney's Magical Express and free WDW transportation can be a good option if you're primarily just going to the theme parks.
You'll normally save time to MK if you use the bus instead of driving. The MK has a huge, distant parking lot, and requires walking, a parking lot tram and a monorail or ferry. Even if you rent a car, I would recommend using the bus to MK.
To the other three major theme parks, it's a matter of luck whether a car or bus is faster. Sometimes a bus comes quickly; sometimes the wait is longer. Buses go to locations near the park entrance, while cars have to parked where a parking lot CM tells you to park. Although there are parking lot trams, the walk to the tram pickup in the lot can be longer than the tram ride, especially at Epcot.
Where a rental car wins is if you're going to other non-MK resorts or off-site locations. If you have dinner reservations at Boma, Cape May, and Artist's Point, you're much better off if a car. If you plan to leave WDW property for shopping, dining, or attractions, using a taxi cab can get expensive.
One thing I've noticed on this forum is that there are some people who would not dream of being without a car. It seems to be more a matter of control than anything else. There are people who hate the uncertainty that comes from not knowing if a bus will arrive in 1 minute or 15 minutes. They would rather deal with driving, parking in huge theme park parking lots, and dealing with getting from their car to the park entrances.
I've successfully stayed at several WDW resorts, including Saratoga Springs, without a car. I use a service to bring groceries. It all worked well.
