The more I think about it, the more I think this is a myth. Everybody say they are the most efficient, but with regards to which metric? The only important metric is door-to-door time.
If I can walk a short distance to the bus stop, have a ride and then walk another short distance to my workplace, then I'm lucky and I don't even consider driving to work.
But if I have to drive to the nearest bus/train station (actually, to the parking nearest the station), then ride to the city centre, then a bus to the suburbs, then a walk in the suburbs... sorry, the car will make much sense, even with the traffic jams.
You're thinking of motorcycle/scooter. All the speed and independence of a car, while taking up only a fraction of road and parking space. And I can still haul lumber and groceries on my motorcycle.
No, especially in north american cities where you can walk few places, cares are another form of transit, like anything else.
Relatively few people actually ride bikes.
"Pedestrians, cyclists and public transportation are the most efficient mode of transportation inside a city" this is completely false in most situations, especially in North America.
You cannot reasonably walk 5Km to work every day and back. The vast majority of people live far from work.
Even with cities that have good public transit, it's not optimal in tons of cases.
Cars - or things like them - are going to stay. They are not going away.
Commuting 5km by bicycle is fine, takes roughly 20 mins if the roads are decent. Using a tram or bus that has a decent frequency it will take roughly the same time, even including a few minutes of walking.
See example: https://www.google.nl/maps/dir/52.1136289,5.0897208/52.08605...
Beyond that, give and take space within the rules. There is no need to go out of your way to make space for cars, but also don't be a jerk and take priority just because you are on a bike.