Yes, it is possible today with existing super charger capable cars by only making some changes in software. Since supercharging physically connects DC battery to outboard charger, the power can flow in both directions or out of the car into the outboard charger / inverter that can be interconnected with solar panels and house loads. This is exactly what the upcoming integrated solar roof / battery / Tesla charger product should be like. I would be disappointed if it's not. To have your 6kWh powerwall instantly become ~100kWh by plugging in your car would be awesome. Also having DC power path in the system would be great as well, giving better energy efficiency between solar panels and car charging.
Self-driving cars that get 100% utilization wouldn't be parked much, except in super-off peak hours when few people need electricity storage (to fill or use). But, in between now and then, a period of a few decades, your idea could work.
Putting together what you and nwdiver said, I think this capability probably won't come out until the grids start asking for it, at which point, it would come out pretty quickly. If the grids never need it, then they won't ask for it. If only certain small grids or regional grids need it but most do not, then there will be sparks, until either they get a workaround or the car companies capitulate. So, according to nwdiver, what we want has nothing to do with it.
The only new information I bring to this thought is that there is a huge benefit to integrating solar panels into roofing material, so Tesla was looking for an end-to-end solution to power the world cleanly. Anything that gets them to that goal will be on the table, and in the view of Tesla, people using grids to power their cars has the potential of keeping coal and oil grid electrical generation in use past when it would have been turned off. Ditto for dams, another thing that the communists in California are trying to take down quickly (I say give it half a century but they want it removed right away, only 5-20 years, and either way, solar and storage are required before that happens). Tesla thinks their stationary storage will help solve that, and they don't see the amalgamated benefit of V2G right now even though "you want to be able to use your house at the same time as your car" from a non-amalgamated point of view. And, as far as Tesla is concerned, if you buy more solar and more stationary storage because V2G is not available, they're getting not only more business but more of the installation of future tech in place. But that only makes sense if they can do V2G in the future.
Bringing this full circle, maybe Tesla hadn't really thought this all the way through, and you are right, but in 2-5 years you should be willing to make a case for it to Tesla. It would help when the charging snakes are installed, because most people don't want to always hook up their car.
Tesla developers live in California in SFBA and GLAA. Both those areas have extended commute hours that often tack on half an hour to an hour to your commute in any direction, if you're lucky, often due to congestion (and usually because of bad drivers). A lot of them probably get home after the sun sets in the darker parts of the year. They are thinking there's no way a car would be able to time shift their electric use enough if there's that big gap in the evening. But, perhaps they haven't run the numbers and seen who does and who doesn't get home at what time and how many of them are plugged in or could be plugged in in the peak evening hours. Some people get off work at 2:30PM while others get off at 6PM. The people who get home early could park their cars, plug in, and keep the lights on for the children and spouses/roommates of those who get home late. And if the cars are plugged into the grid both at work and at home and charging from solar during the day regardless of where they're parked, then this time shifting could be done at all times when they aren't busy driving their car, and there's got to be at least a few cars plugged in at any given moment, even during peak commute. Of course, this will never work when cars can drive themselves and get 100% utilization. People owning their own cars would become a vanity thing that the "rich" do, and they'd be expected to "pay extra", including not having V2G offset their "higher costs".
You could do a vote 
