Ten years after critical mass protests in my city we have a lot (and I mean a lot) more pavements and bike roads (between pedestrian pavements and streets). I manage to get to my work in approximately the same time as with bus along with hundreds of fellow bikers.
If thats the point where you want to draw the line, I guess that it becomes dumb at exactly that point.
But the point of the thought experiment is that it says what you said: it will definitelly happen because infinity is absurdly big number.