I dunno about that,you seem to be mixing horizontal beam antennas Vs vertical antennas and horizontal polarization Vs vertical polarization.
That 6 Db ground gain doesn't apply to F layer paths, (or even Es paths).
As far as the F layer (both F1 and F2), the vertical antenna has a lower TOA and will have a better DX skip distance than a horizontal beam when both are at the same height.
A horizontal beam may produce a better SNR than a vertical antenna because it is not affected (as much) by man made noise which is mostly vertically
polarized.
No, I'm comparing the vertical polarization of my 5 element quad to the horizontal polarization of my 5 element quad.
I disagree with your statement that a vertical will have a better DX distance when it might have a different angle than horizontal but when the horizontal angle is the correct angle the vertical may not be.
I'm also not convinced that a vertical approach of the F layer isn't lossy compared to a horizontal approach.
My experience has found horizontal superior, especially for breaking pileups.
Nor am I in agreement regarding ground gain.
I HAVE found it interesting how often I'm heard over pileups on my first call and over the rest, perhaps there are many others operating vertically?