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2. Many online specialists are juicy live. I don't know any who are capable of beating a big mixed game

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I don't feel that this is an objective way of measuring how good a poker player is. A large portion of the games in your mixed game rotation are games that are rarely spread anywhere else.

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I guess that is the real question. Are the best players those who are among the top players of the most popular game, no limit holdem or is it instead players who master a lot of different games?
Or is it somewhere in between? Is it simply who makes the most money?

If I were to choose the best player my obvious choice would be Phil Ivey who whether it's live or online has beat every different game he has played in. From limit or nl holdem to horse, plo and omaha hi lo. Everything.

It's obviously not suprising that online players dominate nl but if you look at every other game it's actually mostly more or less well known live players who have been the most succesful (online). Plo is where this "battle" is fought mainly.
Now will that change over time? It could very well. We're seeing it in tournament poker, and I understand that's it's a small selective group playing these games anyway.