Premium F isn't going to work for US airlines until they drop the label from their domestic "F" offerings. What "F" means on a US carrier is so ridiculously all over the map that it can never have the value, in many customer's minds, that it needs to command a high-enough price to justify a super-premium service.
On FT, sure, we understand the differences between International anything and Domestic anything. But the domestic carriers do nothing to draw attention to those differences, and I doubt it could be unwound at this time. The damage is done.
In Europe, most "domestic" (within EU) flights don't even claim an "F" section, but rather "business" which is nothing more than a middle seat that's been replaced by a tray. As much of a perversion of the notion of "business" as the US carriers do with "first class." Wonder how much of that has to do with FF redemption? People flying an International leg on a legit C that don't want to see that "mixed cabin" note?