The given answer is perfectly acceptable, albeit a little weak on the 3rd point as has been pointed out, but as an addendum I'd add:
Blaming the Joker would be corruption; the very thing Batman and Gordon have pledged themselves to rid Gotham of. It's still a form of corruption for Batman to falsely assume responsibility for Dent's crimes, but as he is assuming this responsibility willingly it negates the destructive impact to an unwilling party.
If Gordon and Batman were to re-assign the actions of Dent to the Joker, they would be shifting blame onto someone who is innocent of those crimes; although guilty of much greater ones. It's the fundamental act of corruption that they have decided to destroy.
As the Feudal Lord of Gotham, its Lord (and secretly its Knight), Wayne shoulders the burden of exile for what turns out to be both of his personas.
Of course, we see the damage of this in The Dark Knight Rises, when Bane realises this very point: Corruption is Corruption, and both Gordon and Batman are just as guilty of it.
When he reads Gordon's confession, he weaponises this information to undermine the legacy of Gordon whilst venerating the reviled memory of Batman, whom he believes is crippled and watching from afar.
Whilst ostensibly a device to free Blackgate's prisoners (and get a lot of sympathetic soldiers) the genius of this scene lies in its cruelty. Bane destroys Gordon, whilst raising Batman to the heavens as a savior... at the very moment he can do nothing to intervene.
It would be a bitter pill for Wayne to lie wrecked and ravaged, hearing his beloved subjects finally calling for their Knight once more, only for those cries to go unanswered... Brilliant writing, but requires a lot of through-line-following to see the genius of it.