I recently flew from LHR to SEA. The BA flight crew handed out customs form as usual. In SEA I was sent to the new APC kiosks (all passengers on the VWP and an ESTA were sent to the kiosks by the staff, though I have since learned that you must have visited the USA at least once since 2008 with a machine-readable passport to use them). At the APC kiosk amongst other things you get asked much the same questions as on the customs form.
Neither the border control agent who stamped my passport nor the customs officer at the exit of the customs hall took my customs form which I finally still found folded in passport on arrival in my hotel.
So it does look as though the customs forms may be on their way out. YMMV