It just strikes me as trying to make a measurement because you can calculate it, not because it makes much sense.
Depends on what you want to calculate. It's short-term opportunity cost vs. long term. Both are appropriate depending on the decision you are trying to make.
If you want to know what it costs to drive your car today, only count the variable costs. If you want to know whether it makes sense to have a car at all, include the fixed costs and compare to alternatives (like taxis).
I use both ways: The second one made me give up my car in Amsterdam (vs. a taxi and rental budget), the first one I regularly use to decide vs. using public transport on any given day. I also used the total cost per mile to figure out the added cost of upgrading from a very small car to a small car given my expected miles driven.