Not really. With perfect information you know the correct strict equity plays assuming normal opponents. This doesn't give you the ultimate answer, because a player's reads and inference about another player is definitely an input - especially at the highest level - but it is more than enough to give you a winning/losing player at the small/midstakes.
source: worked for an online poker company that had these tools... and far more available to us
I think player-dependent strategy is more important at lower levels because the players are much further away from what you call "normal opponents", so there's far more opportunity to exploit their mistakes.
That's interesting, could you share an example? Most of my search results are anecdotal Reddit threads about how many people cheat in online chess.
From what I've read, they work by comparing the player's moves against chess engines, and if the player is picking engine's choice too often in positions where there are multiple roughly equal moves, they get flagged.