Wow, what a list!
Yes, I do carry all of the card with me in a separate folio in my breifcase. I use this folio to keep the cards, coupons, certificates, upgrades, etc. in one place for easy access. Before my trip, I place the appropriate "cards" in my wallet for the airlines, car rentals, and hotels that I would be at that night. I ALWAYS show the card at checkin, it helps in making sure you get the credit for the activity!
8 airlines, 1 elite, 1 premium
5 car rentals, 3 elite, 1 premium
8 hotel, 3 elite, 2 premium
1 frequent parker program