Thanks for working through some numbers.
My modest intended implication was that if we only care about total sums, where the car is doesn't matter too much, as long as it has access to the grid.
The economics could work out, if the car park charges you more for electricity than they pay the grid; and the grid your home less that it charges the car park.
The car park and the grid both take a cut. For the home- and car owner, this works out to a slightly less efficient battery cycle. (If you convert the money charged back into the equivalent amount of energy.)
Of course, if you are going to use your electric vehicle like as a battery like this, it's going to affect the battery's useful life. The same would happen with the single purpose battery you have sitting in your home.
Now, the performance characteristics one looks for in a car battery and a grid storage battery are different. So I don't know whether using the car battery as a home battery even makes sense. (Ie home batteries can be bulky, but better be cheap. Car batteries have to be light and charge fast.)
On a more refined note, one can play the same game, but only do it during spikes. Ie the car can stop charging during a spike in demand, and even uncharge if the spike gets big enough or the battery is already full.
This won't do much for the diurnal cycle (that we discussed above), but a contribution during the spikiest peaks might already be worthwhile.
My gut feeling is that we will see the demand shaping for charging, but I am more doubtful about whether we'll see cars actively feeding back into the grid.