I'm all for transparency and offering criticism where it is needed. It needs to be done graciously, and if you ask me, privately. Posting OOC criticism can bring negative feedback from others since most would interpret said criticism as a personal attack. Every roleplayer should improve their writing skills, and if it takes a nudge or two to put them in the right direction, why not?

But what also needs to be taken into consideration is that some just don't want to improve, and prefer to play as they usually do. This mentality usually comes from a lack of serious interest in roleplaying. What I mean by that is they don't really find the pleasure in sitting down and plotting the next move of their character, and just goes with what feels appropriate, and perhaps, awesome at the moment; or, like you suggested, they're outright lazy and reiterate what others have written before them.

As to who should be responsible for telling the player what they're doing wrong, I believe anyone who wishes to help others improve. Perhaps the GM won't necessarily mind that player's writing style (or lack thereof) since it does not directly affect the story in one way or another. Thus, the intervention of a player is most needed. So what if multiple criticisms arrive on their end? There's an infamous saying in my country which I find fitting here, and it roughly translates to:

"If two people tell you you're drunk, perhaps it's time to go home."