SwingsitlikeHogan
Major Champion
Your key assumption is the flaw in your argument. It is the players responsibility to put it on the card for exactly that purpose. Up until he tees off any number of things could cause it to change from that recorded somewhere previously.
That's the missing link. I could have played a comp elsewhere that resulted in a change to my handicap but I had not informed the club of that change, so the club comp organiser won't know my new handicap. It is up to me to make sure he does, and the way to ensure that is by recording my (new) handicap on my card. Completely removes any risk of miscommunication etc.