Tony
I follow your logic and in some circumstances I would agree with you. However....
What would you do if the carpet was brand new and somebody spilt a glass of red wine over it? Would you really only clean the WHOLE room? Also, whilst I agree that it's pointless removing a stain and having a clean mark and therefore the whole room needs to be cleaned the opposite it also true.
What if you convince the client that the whole room needs cleaning but then you can't get the stain out which was the whole reason that the client called you in the first place? I'm assuming you would at least clean the stain first and then assuming it came out you would then clean the rest of the room. You wouldn't, surely, clean the whole room and then apologise for the fact the stain was still in the carpet.