A $60k retrofitted transporter van isn't exactly the definition of "independence".
But my post was not about the relative merits of cycling versus driving. I simply wanted to rebut clairity's point that making cycling and walking safer necessarily makes driving slower.
Also, I think I would frequently (perhaps not every time, but at least 25% of the time) beat a driver to the door of my workplace from my apartment because of a combination of cars not actually being much faster than me due to traffic, stop lights, etc. and parking. My parking is so small that it's a lot closer to my building. This obviously depends on where you work, but here it seems to be a major factor. (On second thought this would also depend on which lot the driver would park in. Most would have a long enough walk to make cycling faster or at least about the same. I also haven't done this race, for what it's worth. Anyway, the point stands: travel times for cyclists are not necessarily worse than drivers.)
I'd wager that you can reduce the top speed cars are allowed to travel significantly before the effective speed goes down by much, especially if you can improve traffic flow by e.g. vehicle-vehicle communication.