I respectfully disagree. I think Riot did a better job than you think.
I'll base my arguement off your points.
(1) It's kind of silly to say where he used to work as a warden. Now that he's dead, that kind of detail doesn't matter. Really, this jail could have just about anywhere at any time. For all we know, he could have been a jailer in Icathia or any other ancient civilization. Simply put, we won't be seeing that jail, nor is it important to his story. Sometimes, it's actually a really bad idea to focus on these small details as it hinders Riot's ability to paint a more vivid picture. Only when a characters origions must be clear is it important, such as in the case of say, Syndra.
The more important details here, is how he acted in his past life. He was a sadistic maniac in the past life, and has now been reincarnated as something far worse. His prisoners are now the souls he collects. Once his eyes are set on an opponent, he will not rest until he tortures and kills them. In such a way, he's almost a bit more evil than Shaco. That's saying something.
(2) Now, I would like to bring up the point that Thresh hasn't been fully released yet. His voice overs can be just as important a giving people a feel of the character as the background lore is. Second, characters like this usually are fairly one dimensional. He's a man of his work. In rare cases, what man does is what defines him. Thresh mutilates and tortures for giggles and souls. That very idea alone paints a vivid picture of the Chain Warden.
(3) My good man, these are the times you must make inferences for yourself. He's not mearly from the Shadow Isles because the weather is nice. Thresh has a clear-cut mission. Find the strongest souls in Valoran. Remove said souls from their hosts. Looking at his gear and some of his animations, you can a fairly clear idea of how he does this.
A hint, his lantern isn't really just a lantern. It's a soul cage of sorts. Also, a question. Why is he collecting these souls? What is his endgame? At least, unlike Hecarim and Mordekaiser, we know why he is here. Thresh goes where the strongest souls gather. However, it is a universal fact that we don't know why the Shadow Isles has taken such a sharp interest in Valoran.
However, all signs point to the fact that we may soon be finding out.