This game is all about cycles when you think about the grand scheme of things.
What do these scenes have in common?: first Screamer encounter, the part where J.P. commits suicide, J.P.'s situation in general, encounter with the nun, encounter with Anne in the end, final area in general, just to name a few.
They're examples of history repeating itself, cycles.
Sanchez dies at the hands of Screamer because of a misunderstanding (Murphy thought Sanchez was beating up a woman and tried to stop him), Murphy gets in a similar situation at the end, when Anne tries to kill him (she thought he killed her father), another misunderstanding.
J.P.'s suicide - Murphy talks about all the things J.P. did, J.P. denies it. And once again, what Murphy does comes back to bite him in the ass (like the Screamer encounter) during the nun part in the morgue, he's J.P. and Nun is Murphy, she questions him about all the things he did but he denies it, at first.
J.P.'s whole situation is that he faces his mistakes over and over again.
Final area of the game is once again the example of history repeating itself, cycle. Prison riot happens again, chaos is everywhere and "Murphy kills Frank". I put that in quotes because that's what Anne thinks happened.
In the end, the game is about breaking cycles.
Murphy went to prison to kill the Bogeyman, he agreed to kill another Bogeyman, but couldn't do it, Bogeyman died because of his mistake. He went to SH, encountered Bogeyman, this time he broke the cycle, he didn't kill any again, cycle didn't continue.
That's what some of the endings reflect, that you must break the cycle. Truth and Justice ending is an example of a cycle possibly continuing.
The game isn't just about cycle of revenge, it's about cycles in general. You have to break them, because, you're not "progressing" if you don't.
This is a very interesting outlook of the game but it certainly seems valid.
Just one query: doesn't Murphy kill the bogeyman in the end, hence why Charlie says: "You did it. You killed the bogeyman" Although Murphy does acknowledge the futility of that action responding "It doesn't matter", so in that sense the cycle is broken.
I hated the fact that the truth and justice ending was canon because it is like you stated, it might be that the cycle is continuing. How could Anne be so stupid as to have revenge burning in her heart after everything she'd been through. Surely she'd take it that her desire for revenge against Murphy was flawed but instead it's like she interprets it that the town was there to show her the truth and that in order to correct things, she needs to kill Sewell and get justice that way.