That only catches a subset of ways online poker rooms can cheat.
The server knows what cards everyone is holding. Even if the cards were randomly assigned and weren't changed after the fact, users have no logs of the order of cards remaining in the deck. Its pretty trivial to have software that selects community cards that usually lead to a larger pot.
Wouldn't that show up in a statistical analysis of the community cards? How is your algorithm modifying the community cards advantageously but preserving randomness such that over a large sample size every card shows up at the same frequency? Although it wouldn't be exactly the same, presumably some cards that are less often bet preflop, like a 2, would show up at a slightly higher frequency in the community cards, but still.
The much simpler way to cheat is to just give some players more information. Or, run bots that take up guaranteed payout seats in tournaments and such, which I've heard rumors of happening on certain sites. Or both.
Fake players or predefining winners would work as well.
My point was simply that an online casino could seem completely legit even if you can compile audit logs of every players' hands at the table. Controlling the community cards is completely undetectable and more than enough to push larger pots, and therefore larger rakes.
As far as I'm aware, you would have to know the full list of cards in the shuffled deck before the hand was played to know they didn't change the community cards.
That's not exactly true. It's a non-trivial but not exactly difficult task to design a fair shuffling cryptographic protocol that every participant can validate after the fact.
On the other hand, that still doesn't prevent cheating in the form of the server providing information to some participants via a different channel. There's nothing cryptography can say about out-of-band communications.
So maybe fair shuffling is cute but ultimately pointless.
My point wasn't that a fair, auditable system couldn't be built. Only that we don't have that today, and I'd add that online casinos are incentivized to not build that.
Long term, people store their hand histories and this shows up plainly in analysis.