For poker, people can still play face to face, and it being a game of mixed strategies means it's probably a lot less important that poker bots are better than people than in chess. Top chess players use the computers to set up preparation bombs on their opponents, with rebuttals to moves for specific positions created by the computers. That doesn't work in a game of imperfect information and mixed strategies.
The norm for online chess is to not play for money, whereas the norm for online poker is to play for money, often for large sums.
Of course the game with higher stakes is more likely to attract cheaters.
That is definitely not the norm. Most people are playing recreationally. Heck it is illegal to pay poker online with real money in 44/50 states in the US.
I don't see this, I used to really enjoy online poker tournaments for play-money. It's a fun and strategic game in and of itself with nothing more than minor bragging rights on the line, to me at least. I honestly don't see why it should be any different from chess in terms of purely recreational play. (You could say chess is a deeper game, and that's probably true in some ways, but that's not a positive feature for casuals like me with no desire to invest many hours/years into mastering the game.)
Would you play the same way if you were betting your life savings versus $5?
e.g. I'll lose 100% of my matches against a Chess GM but against the best poker player in the world I could go all in preflop every hand and still win the match ~20% of the time.
Only way to counter this variance is to play lots and lots of hands (Law of large numbers) It could take weeks/months in a single matchup to determine the better poker player.
In terms of playing for real money, in general you'll find more challenging competition at higher stakes. But then there's an incentive for bots.