Another problem with those water heaters is the tremendous amounts of energy they consume. If you've taken any thermodynamics classes you know that in order to have heat transfer, you need driving force (a difference in temperature) a one degree difference in temperature (such as the stove being 70 and the water being 69) would take a while. A larger difference (300 on the stove to 70 on the water) will heat up quite a bit faster.
This is the same reason you put your stove on high when you boil water, not because the water will boil at only the high setting, but because it will transfer the energy the quickest.
So, how much energy do you think it takes to get cold to mild water to shower temp in an instant? A LOT. Judging by how it says 20 amps, that means that at 120 volts it's 2400 watts, that's some juice. And even if you did get an inverter, you'd be looking at around 220 amps from 12 volts, OUCH!
Sorry for the rambling, i needed to take my mind off school for a little while.