I think you're overstating the variance. If you watch high level poker play you will consistently see the same players at the final table of big tournaments. Sure, a few lucky random players will go pretty deep in the tournament, but they just don't do it nearly as frequently as the top few guys.

A competent but not great player has a chance of beating a pro in one session, but it's definitely pretty slim.

When poker players measure variance, it's $$$ over time. And while some pros are indeed good are surviving the bubble in fishy tournaments, none make a perfectly consistent income. Even amongst crushers, the variance can be massive.

For every tournament you make a big score, you crash out of 5 and get min payout on a few more.

Many of the biggest names in poker have been the biggest losers in a given calendar period. For example, Gus Hansen and Daniel Negreanu are two of the biggest winners of all time yet also have some of the biggest documented losses...

Not clear how long your "sessions" are but they have poker tournaments where the same people regularly make it to the top.

Not as regularly as you think. Earnings vary a lot.

As for how long a session is? 8 hours. I made a living from poker for a few years.