I've been Starwood Platinum since day one of Starwood's existence. (I was top tier with the former Sheraton SCI program and medium tier with the old Westin Premier program, as well).
I cannot recall being asked once in the past ten years for my card at any point. I haven't carried my SPG card in at least 6 or 7 years.
Perhaps others have run into glitches whereby they needed their card, but I never have.