I think it's brilliant. Not the first time I've read about this.
A few things, if you find the right storage unit (like my climate controlled one in Elgin);
1) The circuit in there is meant to run higher amperage things. So this shouldn't be an issue as long as you're not running the microwave oven along with an A/C unit or other things. I run my trickle charger/smart charger and two big 500w halogen lights in mine when I'm there at night. Well the trickle charger is going 24/7.
2) Odor(s). Most storage units have a few inches at the top of each unit that are open, to allow the units to "breathe" and they run across all of them in that "block" So there is ventiliation and circulating air. In the case of mine, being a climate controlled unit, I actually have a heating/cooling vent blowing in right over the car.
3) Taking a piss/shower/etc. Get a Planet Fitness membership for $10/mth. Go there daily/as needed. But my guess is, is that if you're in these levels of dire straights, hygiene may not be your first priority...
4) where you could run in to problems is if your storage facility has a nighttime cut-off. mine for example is 10:30PM to like 5am. So you can't get back in between those hours. If you're in there within those hours already (and I have been cleaning up the car), you can get out, just not back in. So if you have an shitter emergency at midnight... Looks like you'll be sleeping in your car until you can get back in in the morning.
I'm not saying I've thought of this before, but logistically, I don't see it being a problem.