If we could fly we would, but it just doesn't make economic sense to fly down from Atlanta with a family of 4 (soon to be 5). So, we have never taken a trip without our car.
However, we have often parked our car and not used it at all. If I were a flyer, I would use WEGOSHOP to get my groceries (takes some planning, but in some ways wouldn't it be nice to have your meals planned out...not day by day, but knowing you have the makings of 5 dinners for example), use ME to get on property and finally using the bus system for all other trips. I guess we consider the buses to be part of the WDW magic. My children LOVE riding the buses to and from Disney (their one chance to sit up really high and see the sights around them without the restrictions of a seat belt I think is the appeal - even though they have to sit still and stay in their seats) and so we just make sure we are never in a hurry to get anywhere. Actually, that is our mantra for all of our vacations at WDW. Get to the parks early in the morning and then we don't have to hurry for the rest of the trip.
If you think you would be doing off site things (Sea World or Univ for example), why not do them early in your trip and combine it with a trip to the grocery store. You can rent a car (I believe at the Dolphin) on site and you would only have to have it for the exact time you needed it. If you aren't going off site for shopping or other parks, I would not even worry about it.
The charges for WEGOSHOP seem sorta steep at first glance sometimes, but they have reduced rates for WDW travelers AND when you value in the cost of a rental car and your time to actually shop - its a bargain! (also, they schlep the goods up to your room for you - woohoo!!!)
Good luck with your plan!
Laura