Why would Finch go work for it after he stared down the camera and threatened Samaritan's death? If anything, working for Samaritan is not even the last thing he'd want to do. He'd probably rather die than work at the behest of a broken system. Also, you could argue that in S3/4, there was a bad guy ending and now S5 is about bringing down Goliath and winning the war against all odds (while suffering massive casualties).
It already calculated but I think that's where the fatal flaw comes in. It's assuming that Finch will comply and work for it without Finch or Team Machine taking drastic measures to prevent that from happening. Not to mention, Samaritan branded Finch with a threat sign after Finch escaped from Greer. So I don't think working for Samaritan is a viable ending. Finch is going to go off the deep end and do anything to destroy Samaritan, and is highly motivated for doing so after the death toll.
Finch at this point is, as this thread has stated, Super Saiyan. Unhinged. The only thing I learned from Lost is that we will always have a constant. A dying Reese explaining to him that Samaritan will only be it's best with him at the helm would push him to that.