> the treshold density in walking distance versus the treshold density in cycling distance will scale quadratically with the distance (since area is quadratic function of the radius), an electric bike that extends your range twice, will result in a 4 times higher "effective population density" for public transport to make sense.
That's exactly the problem you're working against. A bicycle doubles the radius from walking, but a car at 70MPH on the highway multiplies it by 20 or more, so you get hundreds of times the area and consequent sprawl. And ebikes at those speeds are fatally dangerous, so they can't be a replacement.
The thing that can actually be competitive is trains that can go as fast as cars, but then you need the density to fill them.
That's exactly the problem you're working against. A bicycle doubles the radius from walking, but a car at 70MPH on the highway multiplies it by 20 or more, so you get hundreds of times the area and consequent sprawl. And ebikes at those speeds are fatally dangerous, so they can't be a replacement.
The thing that can actually be competitive is trains that can go as fast as cars, but then you need the density to fill them.