Can I answer yes, and no at the same time?
Since everything you have planned to do is on site, you don't NEED to have a car. Disney's transportation system is very complete, and will get you everywhere you need to go, and do so in a fairly reasonable time frame, and it is all included in the cost of your vacation.
A previous poster suggested that driving yourself does not save time. I disagree with that. It won't necessarily save you time on every trip, but many times it is faster to drive yourself. The only park where I feel that buses have a time advantage is MK, where driving means taking the ferry, or Monorail back to the TTC, then the tram to the parking lot, then driving to the hotel. It is generally quicker to get a bus. At every other park, if you get there early enough in the morning to get a spot close to the front of the lots, it will be quicker to drive. Add the convenience of NOT having to stand for the ride home, and driving yourself can become really attractive.
We used buses exclusively for our first 6 trips, even though we had a car with us every time. During trip 7 our car broke down on our non park day, and had to go to the
AAA car care center near TTC. When I picked it up, we were in MK for the day, so I just parked it at TTC and went back to the park, then we did the ferry / tram shuffle to the car, and drove back to our resort, and realized it wasn't THAT bad.
Trip 8, we drove to the parks a couple of times, just to see how it was, and it worked out pretty well. This year, we are staying offsite, and so will drive to the parks every day. I really don't see that as a bad thing. The only real downside I see is having to drive late at night when you are tired from a long day in the parks, but it's only a 30 minute drive, and at least I won't have to stand up
