It's a small city which is very walkable and cyclable.
The centre is, further out active travel links are poor and the aforementioned public transport orbital links even worse, so car is the default choice.
If you want to get around by car a historic city isn't for you; go live in Milton Keynes, Stevenage or similar if you want that.
You'll never completely banish cars from Oxford as a whole, the city centre perhaps, but most of the suburbs are designed for cars and something really radical would have to happen to change Oxon's addiction to badly designed car dependent suburbia with little room for future mass transit corridors.
Removing cars and adding buses instead can't possibly make it worse. One bus takes 70 cars off the road.
You won't remove enough cars on the sections where congestion is a major issue (the narrowest sections of Botley/Abingdon/Banbury Roads for the P&R, the Cowley/Iffley/Rose Hill area also are an issue for non-P&R buses), because it's often orbital traffic for which there is usually no viable public transport option sadly.
Hence why you need at least a few dedicated public transport corridors from the bypasses to the centre (min. east-west + north-south) to truly make a permanent dent in Oxford traffic and provide an attractive public transport option to get Oxon residents out of their cars.