Let me clarify,

Part of being able to board quickly is 'the flow'. If I start breaking up the flow to do various things, your flight will not depart on time.

I was a little hasty with posting "you're outta luck" as I don't actually say that (internet toughness, so to speak). I'll ask them to stand aside and would add the number after I've finished the boarding process. People are given ample opportunity to add their Aeroplan/Mileage Plus/OnePass/etc number, but while they are boarding with ~100 people behind them, is not one.