No I think it makes sense story wise to bring Batman in this way, it's all about Superman becoming Superman and developing his relationship to humanity, where Batman fits in, representing the people who do not trust and fear Superman. And also, to have an older, hardened, cynical Batman (representing the state of the world we live in now) and to have Superman's actions bring him back from the darkness, Superman representing hope, a light in darkness, the best in humanity.
However, I think it could have been better to do the basic idea of BvS, and expand upon it into a two parter, making a Man Of Steel trilogy that follows Superman's arc from the beginning of MoS to the end of BvS, that focuses more on Clark's character. I think the plot, characters, and themes in BvS all would have benefitted from being expanded upon, and would have made his sacrifice more emotionally impactful for the audience.
You would need to add more story, maybe an entirely new plot line to fit into 2 2.5 hour movies. Part 1 could have a little more interaction between Batman and Superman, a misunderstanding but an uneasy truce. Part 2, the first part could focus on the two clashing and the second part the DoomsDay battle. I think it could be interesting to focus more on the political nature of Superman, have him putting himself out there, trying to develop a relationship with not only the US government but the United Nations, with different countries being afraid that the US would use him to their advantage. So Superman tries to hold to a UN pact in which he tries to have a working relationship with the President, where he can cross borders and intervene in natural disasters, but not in foreign affairs. Of course, this is where Luther (a completely different interpretation and actor) comes in, with his political sway, perhaps he is running for President, butting heads with Senator Finch. Batman, who is not as naive and trustworthy as the farmer from Kansas, sees this working relationship with the government as them using him as a political tool and possible weapon, which causes him and Superman to butt heads, as well as Clark investigating Batman's brutality, and being told by the government (through Luther) to put a stop to Batman's lawlessness. Of course, in the final, Superman realizes that he will always be manipulated by men seeking power if he is to continue his relationship with political leaders, and learns that he must act on his own judgement.
I think it would be an interesting venue to explore, that they touched on BvS with the political leaders questioning Superman acting unilaterally, and the senate hearing, but if they really dug deeper into it, it could make for an intelligent, fascinating story, and also would give Superman and Batman a more logical, fleshed out reason to butt heads without either coming off like the bad guy, and touch on some interesting social and political themes, similar to Watchmen.
Also, with an extra 2.5 hours worth of story to fill, they could include another of Supes or Bats' villains, maybe some cameos by some of the Rogues Gallery, or find a way to include Court Of Owls, Deathstroke, or Hugo Strange. But still sticking to the basic arc or structure of BvS
