That's actually a really good question.
Finite capacity means that they will be exhausted provided that there is no opportunity for replenishment of the systems or waste product removal - once exhausted their input is basically zero. Rest most rapidly returns the energy systems to a replenished state, but at moderate-high intensities oxygen too becomes available to assist with restorative processes, but the rate that this is happening is much too slow for the ATP-CP system or lactic acid system to significantly increase their output unless intensity is very low. So once ATP stores are depleted, that is, they're very low, there will be extremely minimal contribution (about <1%) unless intensity drops a lot or there is rest. Because of the complexity of the intramuscular environment (molecules flying around everywhere and reacting with each other), some CP will be used to resynthesise ATP, but not much.
Basically everything that you said above is correct, except that they are never 100% exhausted because they are being replenished, even if it is at the rate of a trickle.
Does that make sense?