None of those will exceed 20mph - public transportation and biking (presumably) follow the speed limit and the average human running speed is 5 to 8 mph. Unless it's a subway or a train.
In a city center, your average speed will be substantially less than 20mph anyway no matter how fast you drive (unless you violate laws, running through lights and speeding) due to congestion, traffic lights, etc. A 20mph isn't going to make much of a change to average travel speeds.
Most likely, however, you're not going to be driving 20 miles in a city center. If you're driving more than 10 miles, you'll probably want to use a highway, and the US highway system is extensive enough that you can.
As for biking, I have less of a problem with people biking over 20mph in the city. (However, you're correct that, in practice, there's no way someone's going to average 20mph for a city bike commute. Most people aren't in good enough shape to sustain 20mph on the flat.) I regularly hit 30-35mph on downhills (say, Central Park at the north end) because I know what I and the bike can handle. Bikes are small and agile (it's easy to swerve and avoid hitting someone) and much less massive than a car.
Obviously I'm not saying that the speed should be 20mph everywhere. I'm talking about dense, residential areas, such as New York City.