Re: "...a man who is older and wiser than Clark Kent": Does this not worry anyone els
I think the intent is to allow them to
A. Continue from Man of Steel where Clark is really just coming into being Superman
B. Avoiding an origin story for Batman because they simply don't need it
C. Gives a new way to approach Batman pessimism vs Superman optimism
I don't see it as Batman mentoring Superman so much as a way of exploring the polarized views between the two. And after the destruction in MoS, I'm sure Batman sees it as a poor performance for Supes first time out, if he doesn't see him as a threat entirely on his own.
Rest assured it's sure to be a conflict/confrontation that becomes a team up. With the number of films Affleck is contracted to play Batman (I think it's 10 films?), I'm putting my money down that Bruce/Batman is the Nick Fury of the Justice League build up.
We'll see Batman cameos post-credits in some films, plus Superman/Batman, Batman films, Justice League for Affleck. So most certainly whatever the plot starts with, it will conclude with Batman and Superman on the same side, but still with different views on their approach.