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Is the white elephant in the skill vs. chance argument room the fact that ultimately, it's not about who wins the hand, but who leaves the table with the most money? That is, skill determines how much $$$ you extract from the other players, regardless of your cards; ergo, chance dealing you good or bad cards can be irrelevant.

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This again is not a valid argument. If this were the case, good players would win the vast majority of their sessions. I win just over 60% of my sessions and I'm a large winner at relatively small stakes. I'm sure the win rate for high stakes players, who are presumably the most skilled, quickly converges very close to 50%. And if 'leaving the table with the most money' proves skill, wouldn't the best players leaving the table stuck nearly 50% of the time therefore prove the predominance of chance?