Agent Spalko said:
A number of reasons:
1) When Dent had Gordon's family at the place where Rachel died, the police had a border already set up. By this time, Joker was in custody. Had they blamed Joker, everyone would have known they were lying. That would prompt an investigation into the other deaths. Batman and Gordon wanted to preserve Dent's image as the "White Knight," giving the citizens of Gotham hope.
I thought Batman was blamed for the deaths of Two-Face's vicitms, not Dent's death. You can easily save Dent's image without having to resort to blaming Batman. You can easily blame the deaths on Marroone's men. Or, you can quite simply have an unsolved crime. You telling me that Gotham, of all places, doesn't have unsolved crimes?
If he was blamed for Dent's death, you would still have plenty of people asking questions.
"Why in the world was Dent here?"
"Why does Dent's gun match the bullets taken from these cop deaths?"
"Batman never uses a gun"
"Why does Batman not have a motive for these deaths, when Dent obviously does.... and it was his gun to begin with"
"Batman was fighting the Joker, when Gordon fielded the call, which lead to his capture. Who, then, made the original call?"
"Why would Batman kill Dent after taking the time to save him from the Joker earlier in the film?
Batman as a killer doesn't hold up in any way, shape, or form. Certainly, Gordon would look pretty bad if it was found out that Batman was really innocent.
Agent Spalko said:
2) Batman wouldn't want to falsely pin crimes on even someone like the Joker.
Yes, because it is morally okay to lie to the public by implicating an innocent person, but not okay to lie to the public by blaming a mass murderer?
Agent Spalko said:
3) After the events of The Dark Knight, Batman can no longer allow himself to be affiliated with Gotham Police without risking more deaths. By "rebranding" himself, he not only severs all ties to authority, he is also "becoming the villain." As Dent is allowed to die a hero, Batman must accept the opposite responsibility. (i.e.- Dent's phrase, "You either die a hero or live long enough to see yourself become the villain.")
The police could just go further in distancing themselves from Batman. If it is necessary for the people of Gotham to hate Batman, what does that really say? That the idea of Batman is something to be despised? That he is in no way a hero? Then why in the world are we bothering watching these movies?
Agent Spalko said:
4) Harvey Dent is a leading prosecutor. If word was to get out that he's a crazy killer, all the crime bosses in prison would have sufficient grounds for appeal. All the convictions of all the cases Dent has ever tried could be overturned, and all the crime bosses would be back on the street. The movie mentions this a few times. In their first meeting, the mayor cautioned Dent that he had better watch himself, because all they need is a little dirt on him and all the cases would crumble. During the scene where Dent threatens the fake honor guard who was actually a paranoid schizophrenic, Batman warns Dent that killing him would put all the cases in jeopardy. Batman reiterates this to Gordon at the end.
Like I said before, since there is zero evidence Batman killed those cops, then it is just as easy to blame it on the mob, or just to have it unsolved.
Agent Spalko said:
5) During their final confrontation, the Joker explains that Batman's weakness is his adherence to rules. Why abide by a code when your enemies obviously don't? Pinning Two-Face's crimes on Batman is sending a message to the public, and it's not a terribly positive one. This also plays into his psychological dilemma evidenced by the line "I've seen what I have to become to stop men like him."
I always thought that meant that Batman would have to break his one rule (killing) in order to get rid of the Joker. (Which of course he already broke at the end of Batman Begins, but oh well.) I suppose you can also use that line when he was illegally spying on every citizen of Gotham, too.