I reflected upon the evolution¹ of the USS Murgatroid's situation. She had originally been stolen by two cadets fresh out of Starfleet Academy, and become an embarrassment to the Fleet – ordered to remain out of sight (cloaked and/or outside of the populated areas and common flight paths of the Federation) and used as a chaotic "dumping ground" for those misfits that Starfleet could not trust in a position of responsibility and/or public scrutiny. (This is something which the Murgatroid had in common with Starbase 688.)
It was only natural that the Murgatroid, out of Starfleet's mind and sight, would get involved with smugglers and other quasilegal undesirables. Starfleet found a way to use this to their advantage when they assigned us a task during their crackdown on alcohol smugglers; I believe a relevant quote used was "setting a thief to catch a thief." This was when Starfleet realized that the Murgatroid could be useful to them, as a ship and crew who could do things and go places that were out of the question for anyone else in Starfleet; while providing Starfleet Command with "plausible deniability" at the same time. It seemed that we were under less threat of losing our ship, freedom, and/or lives to Starfleet Command once they had actually found a use for us … although this did bring us under more scrutiny from them, while at the same time making them more eager to keep us secret and hidden from everyone else.
Not that they had had a great deal of success in that endeavor, given the furor which accompanied our first visit to Starbase 668.
But our "rehabilitation" began when we revealed the infiltration of an alternate-universe Admiral Janeway into Starfleet and single-handedly (against the rest of the fleet, which had been told we were criminals and traitors – on the one occasion when the charges were false!) drove her out of Starfleet Command's headquarters in San Francisco (rescuing the "real" Janeway in the process). Then, with the assistance of an alternate version of myself from the same universe, the alternate Janeway and her vessels were destroyed.
With the passing of our former captain and my promotion to take his place, the Murgatroid was almost given a fresh slate. I cannot predict how Starfleet Command will attempt to utilize us in the future (I still await the Murgatroid's arrival here before I contact Starfleet to report the rescue of Evil Storvik and T'Sorvik), but it seems possible that we are actually going to be afforded and open an official place in the Fleet, hidden from all eyes no longer.
¹It seems unlikely that the term "intelligent design" will ever be applied to the actions of the Murgatroid.