Why does shutting off cold water valve to the water heater shut down cold water in entire house?
If that is truly the case as you reported it, something is seriously wrong with the design of your plumbing system and you are mixing hot and cold water all of the time, which would be costing you a fortune in electricity bills.

Are you sure it was ALL of the cold water lines that were off? On things like showers, bath faucets and in some places, sinks, there is an anti-scalding / temperature balance valve used to mix cold and hot automatically. With no hot water at all, it may have interpreted that as there being too much cold water, so it kept reducing the cold water in an attempt to balance the temperature. But that would typically not be associated with your toilets. MAYBE, if you are in an extreme environment where the toilets might freeze, someone did that to put a little warm water into the toilets too, but I have never seen that.