I find the irrational inconsistency of this policy super irritating. They obviously can just charge the card. I do NOT ever carry the card because I have a 3-card mini-wallet that is life changing.
Many Hyatts seem to have the completely rational ability to just charge the card, so when they don't and I'm not specially prepared with it.. I end up with Citi points x 3 instead of Hyatt points x 4.