Even assuming completely benevolent car drivers (which seems a stretch), i believe that separated bike and car lanes are the only way it should be done. It is unrealistic to expect such different modes of transport (i.e., very fast 2-ton metal boxes vs. completely vulnerable meatbags on frames going 20km/h) to interact well together. If anything gies wrong (again, assume benevolent drivers: the thing going wrong might be oil on the road, a tyre blowout, sleeping driver, etc.) then the cyclist is going to come off second best,
every time. This is the main point to keep in mind. Cyclists are vulnerable, and should be kept away from motorised traffic.
(incidentally, i believe the same in the pedestrians vs. cyclists argument: they too should be separated. But i didn't want to get too off-topic)
EDIT: grammar
EDIT 2: Another point: it's not as simple as you are saying, where people should just be more patient if they're in a car behind a bicycle. That may be true, but when a cyclist falls, for example, and a car "rear ends" them, they are going to be dead with a non-zero probability. The other way around (i.e. a car stalls and a cyclist rear ends them -- this has happened to me) then it's again the cyclist who ends up somewhere between just embarrassed and in the hospital.