I think one of the "chemistry buffs" can explain this more technically that I can, but my understanding is that the CYA doesn't "tie-up" the free chlorine - if it did then it would change to combined chlorine (which is bad).

The CYA does inhibit the FC to do its job as well - so to add to your analogy- it would be two drunk women talking to the bus boy while he is cleaning - making him slower but able to stay around come AM - while the bus boy with out the drunk women (CYA) around would die like a vampire come first light.

If you have some CYA then you still have some chlorine working when it is sunny.