Yes, a sub 2kg 200-600 with f5.6 at the long end is a big ask for sure, but with some design effort I don't think impossible .....
Most of the long supertelephoto exotics (Nikon lagging) have now gone to a lightweight objective long optical train design with dense grouping at the rear of the lens.
The f5.6 objective at 600mm would be 107mm diameter (the same as a 300mm f2.8). This would have a 26.5% bigger area than the 600/f6.3 objective of 95mm, so careful attention must be paid to the optical design to minimize weight at the front end. Thin aspherical elements and very high spec ED glass (synthetic fluorite equivalent) would be required along with lightweight chassis materials.
Using CFRP, Whisker Titanium Graphite, and Magnesium Metal Matrix Composites (either Carbon Fibre or Titanium reinforcement) should get the job done. The amount of these materials used is fairly minimal, and given that Sony wants about $2K for its 200-600, I think economically viable at that market point.
Manufacturers really need to realize that light weight is where it's at and get with the program. We already have sub 2kg Third Party 150-600 supertelephoto zooms of f6.3 aperture at the long end. The last thing we need is more duplication in the market ...... we need advancement !
For comparison, here are the lens construction schematics of some current lens offerings:
Nikon 200-500 f5.6 2300grms 268mm long 19 elements /12 groups
View attachment 707369
Sony 200-600 f5-f6.3 2115grms 318mm long 24 elements /17 groups
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Tamron G2 150-600 f5-f6.3 1990grms 258mm long 21 elements /13 groups
View attachment 707371
Canon 600 f4L IS III 3050grms 448mm long 17 elements /13 groups
View attachment 707372