For anyone to “do the math” (seriously?) they would have to be able to price out all the components on the board and then somehow know about any deals nvidia had in place with the suppliers for component pricing in bulk, which they obviously couldn’t know. So anyone chucking numbers about is just guestimating at best. The cooler alone is a custom job that nobody knows the pricing of or who even manufactured it.
The heat sink itself isn’t really all that elaborate either, it’s just a long heat sink on a short pcb with the fans in an unusual config, cards from sapphire were doing this back in the fury days minus the fan on the back of the card.
They're estimates in some cases, sure. But most of them are going to be pretty accurate because absolutely none of this is unique to Nvidia and insiders can leak info and make reasonable inferences.
We do know the FE had an expensive cooler design and Nvidia did R&D to get that working along side a custom PCB layout that is different from the reference design. We know the sale value of these cards was deliberately price fixed, they even released those cards for sale through a retailer in the UK (I can't mention due to rules on competitors) and the prices were still price fixed. There's only one reason to do that, it's so you can have marketing of your FE product which they put out at good prices and cool and sleek looking new cooler design and it all looks great on paper. All of that effort and engineering at the end of the day is to allow the marketing people to push VthisV in your face when the product launches.
Another thing, the AIBs were complaining to Nvidia that the kit for the GPU and memory they buy from nvidia, plus the other component costs and then having to use a specific RRP in some instances, means in many cases they were barely making a profit from the manufacturing. So there's already thin margins at play which means Nvidias own product doesn't have to be much more expensive to really not be profitable for them. I don't even see how this is controversial, this is like marketing hype 101, being able to show off some vanity project that underprices and over delivers is fantastic for building hype which they did like crazy.
IF the FEs were money makers for Nvidia why don't they just continue to make them and cut out the AIB middle men and continue to eat into that profit? None of this makes any sense from a financial perspective, If nvidia were making cash on this they'd ramp up production not discontinue it. I'd love to have gotten an FE at launch rather than an AIB, but that's the whole point, most of us were doomed never to get one because the deal is too good.