God, I hate how trendy it is to defend villains like this. Bro, the fire nation only ended it's campaign because of a coup. Sure, they got their asses kicked during the comet, but the last thing on any occupied kingdom's mind is "hey, we should seek justice for that one roving band of teenagers!" This is ESPECIALLY true of Ba Sing Se, where there was an unironic puppet monarchy being propped up by the secret police. After being liberated by the white Lotus, the last thing their leadership wants to acknowledge is the time teenage spies got their government to defect to the fire nation.
Azula and Ozai go to jail because they're psycho and a legitimate threat as possible usurpers. Dissenting war hungry fire nation citizens aren't going to turn to Mai and Ty Lee for serious political subterfuge.