The thing about Rei that works, is initially, he's very much out to pursue a specific goal. In this case, finding the man with seven scars on his chest. (Kenshiro has seven on his chest by the way!) and killing that man. Apparently such an individual killed Rei's parents and enslaved his sister!
Of course it turns out NOT to be Ken and the two managed to join forces to kill those who've done these terrible things.
The thing I like about Rei though, is his change. He becomes concerned for other people. He sees the value in what Kenshiro is doing. He grows to care for Bat and Lin and others in a short time. He understands that its not just about doing only what he wants to do.
And that makes him a perfect example of how some players should fit into the game. Sure it's all fun to be the 'Wolverine' or if this was the 90's, the 'new' Ghost Rider, but in a role playing game that's not a solo game, you need to have hooks that fit in with the other players. You need to be able to engage them. Even if your initial concept is lone wolf, you need to be able to have hooks that go into the others.
For example, lone rogue whose only goal is wealth? Role playing an appreciation for what the other characters can do if only as a nod to the fact that a group can gather more wealth than an individual rogue can, is the way to go. "While I may not appreciate the noise that this armored buffon makes, I admit that his ability to destroy ogres and hill giants is quite useful in the liberation of their funds."
A wizard whose only purpose is to find more and greater magics to master? "While Amar is a fool for worshipping the gods instead of magic, I admire the fact that his ability to channel positive energy saved me the trouble of having to pull out real arcane power to destroy that lich and its minions."
You have to role with it to roll with it.