Your cycling fallacy is…
“People do all sorts of long journeys that just can’t be done by cycling”
While it's obviously not practical to cycle for all journeys, many journeys which are currently made by other modes could – with the right infrastructure – easily be made by cycling.
For example, almost 40% of journeys currently made by car or van in Great Britain are under two miles (which would take about 10 minutes cycling). Half of all commuters in England travel less than three miles to work (about 15 minutes cycling).
With the right street design, most people could easily cycle those distances, with about as much effort as walking. Cycling can also make trips that are currently walked much more quick and convenient.
Good cycling infrastructure can enable some people to cycle for even longer journeys; long-distance and inter-city cycle routes are common in the Netherlands and other European countries.
While most long journeys will still be made by bus, car, or train, there is clearly plenty of scope for the vast majority of journeys, which are short, to switch modes. The fact that cycling is impractical for some long journeys is not a reason to fail to provide infrastructure to enable cycling for shorter trips.