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There are variants. The poker variants that are popular are popular exactly because there is so much more chance. The edge that skill gives is less in Texas Holdem than Omaha Hi-Lo. Which is why you see the former more than the latter.
Not really. Source: Omaha High Low (8 or better) has become surprisingly popular at my local casino, and the edge for skilled players does not seem to be any greater. Limit poker has thinner edges than no limit, but NL has been the ocular game.
Source, my brother-in-law is a WSOP champion in Omaha Hi-Lo. At low levels of play, the edge for skill isn't so big, but once you get someone who knows the game the edge goes up.
Tip, one of the best positions to be in is going for both hi and lo while an opponent thinks they have a lock on one of those. They feel committed to matching any bet, but you're going to walk away with 3/4 of the pot.