The need for a car in Ecuador is an ongoing topic here. I plan to do without, as I am doing now in the Philippines, but each of us has different circumstances and different wants/needs.
Here's an article by an American couple who moved to Ecuador and were surprised by how little they missed owning a car:
Every couple of weeks we'd get the notion to visit some famous landmark or geographic oddity or just go out sightseeing, and we'd kind of wish we had a car for a few minutes. Then we'd either take a taxi or hire a driver. (You can have a private driver haul you around all day in our part of Ecuador for about $10 an hour.) Adding up all our transportation costs for every trip we decided to take didn't even approach the cost of maintaining and insuring a car over the same period of time ...
Their experience pretty much parallels mine. I had owned a car or ready access to one for almost fifty years before moving here, and I am now delighted to be free of the costs and responsibilities of auto ownership/use.
The authors of the article are in a small town, but I think the same will apply (perhaps more so) in Quito.