Most of your proposals can be detected by statistics:
- [...] just to alert you to when your position is strong. Oh, so you are a player that never misses a win? Hmm...
- [...] avoid traps in early games. Now you are a very strange player that never blunders during openings but blunders normally later on. Suspicious.
- [...] just for the occasional move. How do you know what move is that? Are you implying you never make _big_ blunders (but make plenty of non-huge ones)? Also suspicious.
In general, there are many signals you can collect. If other users are complaining about a player then you analyze them, and if your signals say "suspicious" then... you caught a cheater. If nobody complains about a particular user you don't do anything because it just doesn't matter.
Not bad! Yeah, wouldn't be surprised if those are part of the detection algorithm.
I would take longer to detect a cheater who is a bit more sly and only cheats on 5% of moves or less (the odds that someone would match a particular engine 99% of the time its pretty much zero), but over time, yeah, this would work.
I suppose another way to put its is that it's difficult to detect this sort of cheating from a single game, but not difficult to detect it in 100 games.
It seems like most of these would just detect when a player was unusually strong, which of course unusual things are suspicious but they can also be the case that some people are unusually strong.
The point is that in chess there's some variance between the opening/tactics/strategy/positional strength of players at the same level, but not _that_ much difference.
To cheat convincingly you have to boost all those facets at the same time, because otherwise you'll just give yourself out. For instance, nobody is extremely sharp at tactics but severely lacking (human-understandable) strategy.
Engines will help you in opening and tactics, but not too much in the positional/strategy game (they make good moves, but oftentimes it is just impossible for humans to understand them without very deep study, meaning they would never be casually played in an online game).
Another example, regarding cheating but only on the openings: even GM's make mistakes during openings. If you play openings at that strength level but then you often lose won endgames it is clear to anybody who knows the game that you are cheating (because opening theory is much wider than the standard endgame theory).
Finally, since you are not at the level you pretend to be whilst cheating, it gets very very complicated for you to know what you can or cannot get away with.
- [...] just to alert you to when your position is strong. Oh, so you are a player that never misses a win? Hmm...
- [...] avoid traps in early games. Now you are a very strange player that never blunders during openings but blunders normally later on. Suspicious.
- [...] just for the occasional move. How do you know what move is that? Are you implying you never make _big_ blunders (but make plenty of non-huge ones)? Also suspicious.
In general, there are many signals you can collect. If other users are complaining about a player then you analyze them, and if your signals say "suspicious" then... you caught a cheater. If nobody complains about a particular user you don't do anything because it just doesn't matter.