The water comparison example above works fine until you get to the part about opening the tap further and bursting the pipe. The water pressure is already applied to the pipe whether the tap is open or not. (So voltage is already applied to the escape no matter what hte current draw is.) The limiting factor in the water example is the capacity of the pipe to flow water (friction, or resistance for votage). Measure water pressure against the top edge of a swimming pool, it'll be the same as against the bottom of the pool. (Equal pressure in all directions in a body of fluids, if the fluids are not in motion.) So, the capacity of a battery shouldn't make any difference to the ESC as long as the current drawn, and the applied voltage are within it's ratings. Cooling an ESC shouldn't be a 'biggy' as long as you don't try to 'push' the thing further than it can be. How far is that? Depends on what the designer used as a margin of error ("fudge factor" = technical term). The published rating is/should always be lower than the absolute maximum, just good sense, which assumes the manufacturor has good sense...
- 'Doc
PS - Oops! After reading the above, the 'pressure already applied to the pipe' does depend on where the tap is, the top or the bottom of the pipe. I assumed the tap was at the bottom end. The electrical part still holds true though.