Moash did eventually murder Roshone too though, didn't he? Yes, what Roshone did was horrible, but I can understand why Moash was more demonstrably disappointed in Elhokar than Roshone. I see it as being similar to Kaladin seeing lighteyes in Alethkar (in fact, the very same Roshone being one of them) and thinking, "The light eyes on the Shattered Plains would never do this, they would fight with honor." That kind of thinking is naive and unfounded perhaps, but regardless the higher the expectations, the more disappointing it is when people fail to live up to them. Elhokar is the king; he is supposed to be better and he sets the precedents and the tone for the nation. He is much more visible than Roshone; he is making a statement to Alethkar about the indifference and callousness of the lighteyes by killing Elhokar that he would not with Roshone, so politically it makes sense.
I appreciate that Elhokar was trying to better himself at the end and I do think it is sad that he was killed before he could get further on that journey, but I don't think he really started out as a GOOD person. He had quite a lot of personal improvement to do. Dalinar can say he was deceived by Roshone, but the fact of the matter is that he still forgot two elderly people and left them to languish in jail. His negligence was an abuse of power and a miscarriage of justice. He is the leader of an entire nation, and negligence is not acceptable. I work in healthcare, and it feels to me that it would be similar to one of my coworkers abusing a patient and a supervisor not only allowing the abuse but making it possible and giving that person the avenue for that particular form of abuse. That supervisor, even if they themselves did not do it directly, had that person under their authority and do bear guilt for knowing and letting it happen...and caring so little that they just straight up forgot to resolve the situation or make any true amends would make it so much worse. It is so insulting that he just...forgot. I'd be furious with him too.
Not that I do condone him killing Elhokar (and even more so I do not condone turning on people who had once loved you and given you hope when you had), but I can understand the anger that triggered Moash to become a villain. Did he then take that anger too far? Yes, but he's a villain so villainous actions are expected. When in Rome, I guess? Lol.