Does seem to me Starfleet doesn't see itself primarily as a military organization. Sisko's ship the Saratoga
also might well have just been one of many summoned best speed to Wolf 359. For huge vessels of exploration, like the Kelvin
and in theory the Enterprise-D
families make more sense. Still, it wasn't Sisko who commanded Saratoga
so he can hardly be blamed for her tactics.
And I personally don't see how hiding a character's sexuality is "Exactly how it should
be done" (emphasis added). It might be appropriate of course. But so might a character in a relationship, or one who flirts.
I personally don't see how a character with a criminal past is so very unbelievable, even a criminal career in which they were never caught. The Federation's institutions aren't perfect after all. Depends on the specifics of character and story. DS9 even had an ep where a traumatized Vulcan officer in Starfleet became a serial killer. And one of Babyon 5
's very best episodes deals with a man who discovers he had been a serial killer, was caught, and had his memories wiped as part of the sentence for his crimes. Both of these made for powerful stories, although I'm not suggesting either one be copied.
But I can imagine a good story in which a ship's doctor had a past that dark, and undiscovered. One detail that springs immediately to mind would be his/her assignment to the starship USS Redemption
. Okay, a bit heavy-handed but no more than Voyager
. The trick is to make sure it all makes psychological sense in terms of character and to weave it into stories. Mind you, the discovery of same should mean the loss of that character under normal circumstances. So you have to keep it a secret or come up with some reason why Starfleet doesn't rip off their uniform in record time and kick them out! A good reason preferably. Might prefer a backstory where this person was caught and rehabilitated.
Bottom line, I don't think a criminal past necessarily precludes a character working as a regular on a Star Trek
series. Tis all in the details.