If you would downgrade from FB platinum to, say, FB entry (the cheapest card in the lineup). Would the trips that you have already booked with the Plat card be covered under the travel insurance that came with the Plat card, or, the insurance rules of the Entry card would apply?

Most people here likely have a bunch of flights already booked...it would not be great of the Plat coverage would not apply for those, just because you want to switch from FB to Regular Amex..