There weren't very many options available to begin with, and all of them had some big negatives:
1. Let Zife, Azernal, and Quafina remain in office for that last year of the presidential term, and ensure that he never runs again (if he wasn't already not going to run). That's right out, because it basically means that they do get off scot-free, as well as remaining in office with the potential to cause even more deaths and crises, not to mention that the possibility remained that someone would reveal/discover the information sooner were they to remain in office.
2. Force the three of them to resign, then allow the procedures set out in the Articles of the Federation to select the next President. While this also somewhat lets them off without penalty, it gets the three, responsible for the deaths of millions as well as a serious abrogation of an interstellar treaty, out of office and out of positions where they can continue to cause damage or have the potential to cause damage. Further, it allows the process of government and election to proceed as it should, namely with the Federation Council and the citizens.
3. Allow everything to be revealed. Not only would this cause horrific strife within the Federation (as the leader is, in effect, a war criminal, and putting him on trial in a Federation court would have been like putting Richard Nixon on trial for Watergate), but also leading to serious interstellar consequences (an almost-certainly immediate war with the Klingons, not to mention intense disruption of diplomatic efforts with other countries, possibly leading to a war on more than one front with more than one enemy. Who's to say that Azernal didn't do something similar with the Romulan/Federation border? Or the Cardassians? Or any other interstellar power?)
Ultimately, the option that was chosen was the one that took care of the situation with a minimum of upheaval, while also preserving the unsteady and fraying Khitomer Accords and preventing any further conflicts.
Would those involved have preferred to be open and allow everything to air? Probably, but then they'd have to deal with the consequences of being responsible for those crimes causing a horrific, bloody conflict on the level of the Dominion War. Between leading the Alpha Quadrant to a galactic dark age and the deaths of billions for the sake of "principles" or "conscience" or doing something distasteful in order to preserve the balance and ensure conflict is avoided, I'd do the latter, because principles mean nothing if the reason you have them is obliterated. Sort of like the conflict Sisko has during the Dominion War, as depicted in the episode In The Pale Moonlight.
This shows that just because Starfleet forced President Zife and others in his cabinet out of office, instead of going through the civilian and/or military justice systems, doesn't mean that they are immediately "dishonorable". On the contrary, by doing it the way they did, they did the right thing by ousting an individual who didn't deserve the office he held.