Certain versions definitely had souls. As to why he didn't have one, I don't know. Maybe because his origin(at one time) was that he is just some type of clone, that kept getting killed and cloned over and over and getting stronger and stronger. So maybe that made it so he did not have a soul.
But Doomsday getting a "soul" made him literally weaker. At least it was that way with Doomsday Rex. There was some different version of Doomsday who eventually became a hero, that version probably had a soul.
I don't see it as a botch, you could just say for the purposes of the fight Doomsday can use the armor. Or you could give it some kind of interesting spin: Lex Luthors soul is in possession of DD's body, or something along those lines.
Dr. Fate is another story because the Destroyer was created via magic and he's a powerful magic user, so he'd probably wind up a lot more powerful in the armor then someone like Thor would be..