luck and skill are orthogonal!
Not quite. I certainly agree they are not parallel, but I don't think they are orthogonal either.
Anyway, they cannot be orthogonal, because the game is evaluated in a one dimensional scale (loss < draw < win), so you can project their influence into this linear scale and orthogonality is lost.
In less ridiculously abstract terms, if a game is "each player throws 100 dice, the one with largest sum is the winner, in case of equal sums, the winner of a chess match is the winner" you could argue it is high skill because chess is, and being better at chess improves your odds of winning at this game. However, luck is such a large factor, that skill influence is basically negligible.
So, I think the argument of "opening luck has a too large influence on the outcome, to the point that it eclipses skill" is valid. If the condition is true is a different discussion, and probably the discussion that makes sense. It definitely feels true in some cases, and shuffle luck is definitely more important than skill in a significant portion of the games. Identical starting hands is an attempt to reduce that factor, an attempt that I agree does not reduce skill. Reducing shuffle luck altogether is less likely to succeed, because you also want to avoid analysis paralysis and shifting focus from the actual game.
I don't like the "start however you want" because of the shifting focus, although it is an interesting variant to try. Also, I feel like in a significant portion of the boards it would induce too much AP.
I like identical starting hands in principle, but I don't like that it increases, though slightly, first player advantage. One of the advantages of 2nd player (and later players in general for >2 player games) is knowing the opening distribution and the buy. Knowing that there are identical starting hands eliminates one part of that advantage.