He's a special effect. A memorable design as you point out, but one-note.
Some of the best stories with him have been with writers who try to move him on, Paul Cornell is a good example. But the problem with him is that as terrifying as he can (occasionally) be, you can only do 'Death of Superman' once.
When they created this character back in the early 90s I don't think anyone in the Superman office had any idea where he came from, they just needed a special effect to kill Superman. So like a lot of mysterious new villains of that era what you got was a special effect, an evil force that came out of nowhere and was seemingly invincible, unfathomable - Onslaught was an example of this type of character.
So I don't think they had an origin to begin with. When Dan Jurgens cobbled together a backstory for him in 'Hunter/Prey' he connected him to ancient Krypton, a curious backstory was revealed concerning a non-native to Krypton called Bertron who brought the fetus of what eventually evolved to be Doomsday, But to this day that strange origin has never been developed any further - Where did Bertron come from? Where did he come by this fetus that became Doomsday? Why base himself on Krypton? Who were the nameless Kryptonian's who assisted Bertron, and why?
There was a lot there that has been left unexplored. And at this point it probpbly doesn't matter...
Doomsday was best when had no back story, was just a mindless destructive force of nature!