Are you saying you wouldn't let kids swim with the FC down to zero?
Well, I sure wouldn't. With a zero FC, there is nothing sanitizing the water. Maybe it *JUST* hit zero a few seconds ago, and nothing is alive in there, but more likely it's been at zero long enough for some serious bacteria to grow.

Either way, once the bird droppings hit, and whatever airborne nasties settle in from blowing over the neighbor's trash cans, and swimmers start tracking in dirt and GodOnlyKnowsWhatElse, you have an unhealthy bacteria culture situation in a hurry.

Remember that it's not just about algae. Its about sanitization.
Algae is just nature's way of trying to keep you out of an unsanitary pool.