This is actually a good question although the comparaison with full fare Y and full fare F is not correct.
I regularly pay Transatlantic F fares but i have never paid 12K for F.
You must first understand one thing. These are (internet published )international First full Fares. Those fares are almost never taken as they are the last seats on the plane and have no restrictions at all.
if you buy first buy it at a specialised travel agent because they have the exact prices in their system.
a first fare depending on the company can vary very much.
recently i flew BA
and their first fares are around 4400 euros/dollars roundrtrip depending on the route max 5000
on the other hand only has First fares at around 6000-8000.
I know AA
is very expensive. their C class on cdg-dfw is already 5500 so it really depends on what route you fly,aircraft and if they have 3 class cabin.
so instead of flying from cdg to dfw you fly cdg-lhr-dfw in first on british and pay even less than on AA
in my opinion they should have only 3 fare ranges
eco 250-1000,business 2-4000,First 4-6000