I think this may be more a "it's the thought the counts" moment. Yes, Hawkeye mentioned a democratic trial, but after it is mentioned (as you stated in your question), it is not brought up again.
Perhaps in the universe of FMA:B a trial actually went underway, but it happened after the events that were told to the audience, and thus we did not hear about it.
In addition, you have to remember that Mustang was blinded at the end of the series during the climax fight with Father. From the wiki, it states:
After the battle with Father is over, Roy is treated in a medical center, conversing with Dr. Knox. He informs the doctor of his disability, and states that he will have to retire. He decides to pass the title of Führer over to Grumman. Knox then informs Roy that Dr. Marcoh was looking for him and brings the doctor over to Roy. Marcoh informs Roy that he has a Philosopher's Stone which Roy could use to regain his eyesight. Roy initially refuses, but Marcoh say that he has a plan in which they and the Ishvalans (referring to the souls in the Philosopher's Stone) can work together. Marcoh says he'll hand the stone over on the condition that Roy changes the Ishval policy, allows the Ishvalans to return to their homeland, and allow him (Marcoh) to live in Ishval as a doctor. Roy agrees to Marcoh's demands.
Either Mustang can live with his new disability (blindness), or he can heal and atone for his war crimes by rebuilding the Ishval community he previously uprooted and destroyed. I think that either of these punishments are adequate enough for Mustang's war crimes, and perhaps the writers of the anime/manga felt that these would be enough to avoid an actual trial.