GPU should be about $200 at TSMC (400-450mm2).
+ about $150 for the pcb, cooler and other stuff, I didn't consider
Times a 1.6 to 1.75 factor if they like actually being profitable (operations, rnd, sales, marketing, ...).
So about $1.5k, I guess.
Multiply that with a .33 "screw the competition" factor and my initial guess is almost spot on.
.
Real problem:
The largest GDDR7 package money can buy right now is 3GB. That's a 1376bit bus right there. GL fitting that to a sub 500mm2 die.
In the future you could put that amount of vram on a 512bit bus, tho.
Also normal DDR is getting really fast atm. 8 channel can already challenge most vram configurations. Maybe it's time soon to switch back to swappable memory.