I often find it useful to look at systems in terms of pressure distributions. I don't know about parking lots, but looking for seating in trains is similar. There I visualize people as molecules in a gas. They tend to distribute evenly. However the passages between cars are high-friction so pressure differences show there. As I walk between cars I can gauge the pressure differential and whether it's sensible to continue walking that direction.
For the parking lot it would have to be a column of air. As you descend towards the entrance, pressure increases. The rate of the pressure increase forecasts saturation.
It can be useful as a basis for discussing provably poor parking spot seeking algorithms; since an optimal algorithm depends on so many variables that's usually past the point of being worth splitting hairs.
It seems to me that instead of using physics inspired reasoning on the problem, it would be better to model it as a multiplayer game of perfect information. Under suitable simplifications, a Nash equilibrium exists, but then the question becomes: how close is reality to this simplified scenario?
You can always make choices that make bicycles practical, has been a very good ROI for me, but for the last 70 years many people have made investments based on the premises that bicycles are not practical. With so much sunk capital in something, alternatives might seem impractical.
I commuted 6 years by bicycle in Luleå, Sweden. Now I live further south and the best snowfall I get is about a meter thick, sure that's an inconvenience but with good plowing that's no problem. The cold can be an issue, but even at -13F/-25C with proper clothing that is actually preferable for me, I've heard this can be bad in Chicago.
A one hour commute in the winter is not for everyone, but dropping by the store 1-4km away is practical.
For the parking lot it would have to be a column of air. As you descend towards the entrance, pressure increases. The rate of the pressure increase forecasts saturation.