So, I started reading Mistborn not longer after finishing [Wheel of Time]...
Why does it seem so intentional that they're a parallel? That Mistborn is set in a 4th age a cycle in either direction from Randland? Well, more the close of the 4th, beginning of the 5th, as the influence of the Dragon/HoA is ending. The Deepness is basically exactly the Dark One, what the Hero of Ages had to go through reminds me very much of Rand's tribulations, hell, his diary could have been written by Rand himself. And what did Rashek do after killing off The Hero of Ages? He became Nae'blis and quickly established unquestioned rule over the world as God-Emperor.
Even how the Deepness attacked the Hero, trying to convince him he was insane, filling him with doubt that he could possibly succeed, or rule, it totally fits how the Dark One tries to break his foes rather than simply destroy them outright.
Mistborn was inspired by my love of the classic fantasy stories from my youth, Wheel of Time at their forefront. The original idea was for a Shannara-esque fantasy epic where the heroes lost at the end, but I decided (for many reasons) this wouldn't be fun to read or write. The idea simmered for a year or two until I realized it would an awesome backstory for the heist story/epic fantasy mashup I'd been developing.
And so, I worked to make Rashek's story as resonate with classic fantasy epics as I could. I wanted that resonance so that I could play with the tropes of epic fantasy.
Remember, Wheel of Time was a huge influence upon me as a youth and a writer. I knew I couldn't just write ANOTHER farmboy saves the world story, as I felt those had been done (and done well.) I wanted something that had one foot in this, however, and one foot in a more contemporary style of plotting and worldbuilding.
So everything you're noticing is indeed intentional. Mistborn is my vision of a world where Rand gave in. (Or where Frodo kept the ring, etc.) I wrote the trilogy primarily in 2004-2006, ending one year before I was chosen to finish the Wheel of Time, which makes the parallels even more interesting.