Maybe not so weird, but a 800 F/5.6 PF the same weight as the 200-500 or 500 pf and same price.
Same as 200-500 and 500 PF.... those are two completely different priced and weighted lenses
I'd love an 800 f/5.6 PF. I'm not sure what I'd be willing to pay.
The conventional, i.e. non-PF, 800mm/f5.6 AF-S VR is $16k. PF will only significantly added to the cost. A 800mm will have a much larger front element than 500mm.
Physically it is impossible to keep the size and weight down, unless it is 800mm f8 or even f11, ALA the Canon version.