I can't speak for him, but I can say this for me: I prefer a game where policing stats is not at issue: where players play the PCs that are described by the character creation process, and as described by the rules, they do their best to play a character with a low intelligence as if it had low intelligence, a character with a low wisdom as if they had a lot wisdom, etc...
I agree... up until the colon... I would argue that after the colon is an example of policing how someone at your table is required to roleplay. Maybe that policing happens just once at session zero, or maybe you need to speak to a player outside the game for violating this requirement (as you go on to say below), but it still is policing.
Where players play themselves, rather than their PCs, I usually have a conversation with them first to raise awareness and offer suggestions.
If the issue persists, I take it out of their hands by using further abstraction. As an example, if a PC is ignoring their low intelligence, instead of telling them a riddle, I tell them the PCs are given a riddle, and then make the riddle answer reliant upon an in game fact that the player can't know. For example, the riddle might be delivered in dwarven, some of the words might be synonyms for nautical terms in dwarven, and those nautical clues might provide the context to realize that the riddle is describing the ship of a certain famous Dwarven Mythical Pirate. And, if the player is exhibiting unreasonable levels of knowledge about the monsters in the setting, they'll start to encounter variants of those monsters with different stats, or homebrew monsters that they will not know anything about.
In the end, D&D is an RPG - a role playing game. If you're not playing the role described by character creation, you're not playing the role playing game described by the books.
I'll refer us all back to the definition of
roleplaying as explained by rules of D&D 5e: "
it's you as a player determining how your character thinks, acts, and talks."
Yes, the player can certainly use the character creation process to inform how they play their character. To be clear, I don't think I've seen too many players
not do that. But, again, I'll stand by the assertion that the 5e DM has zero role in telling a player how to play their character. IMO, it's a big waste of DM time and energy to worry about how someone is playing their character. Someone's INT 6 character, for example, coming up with smart tactics does not rise to the level of violating the goals of play, IMO. To argue otherwise, to use your logic, "you're not really playing the role playing game described by the [5e] books." I don't subscribe to your logic, though. If you want to police adherence to PC stats for your own roleplaying purposes as a 5e house rule at session zero, and that is fun for your table, go for it! That's a big goal of play: for everyone to have fun.
As for a player "exhibiting unreasonable levels of knowledge about the monsters in the setting", that's a metagaming issue. I've learned that - to paraphrase Fight Club and
@iserith - the best way to deal with metagaming is not to worry about metagaming. Players in our games are welcome to use whatever knowledge they want. However, what the player, and hence their PC,
thinks they know and what is actually true in the game world could be very different things. If the player, via the PC, acts rashly without testing metagame assumptions in-game, they might find their PC in dire circumstances. Monster variants are one way to deal with that. Players learn very quickly to engage with the game world rather than act upon brash metagame assumptions.
Brings me back to this point which ties back to the OP: If a DM finds themselves saying: "Your character wouldn't know/do/say that", immersion is broken.