There are two competing narratives for why there is a SC. There is the "popular/press pushed" version, which you summarized well; and there is the official reason, with an unstated premise.
The official reason is that it was in the public interest to have an independent body (the DOJ being beholden to Trump, cough cough) investigate the allegation that that Trump campaign colluded with the Russians. The unstated premise is that Rosenstein is beholden to Trump, and therefore conflicted.
The popular reason is supported, in the press, by cherry-picked reference to Trump's interview with Lester Holt. He wanted the Russia investigation to stop, so he fired Comey. But in that interview, Trump said expressly that he wanted the investigation continue, he thought it might take longer even, now that Comey is out.
Now, the reason for Mueller in fact might be that Rosenstein back-stabbed Trump (along the lines of working in cahoots with Mueller and Comey) - and that version is supported somewhat by the Trump/session kerfuffle around the time Mueller was appointed.
I'm hoping the truth comes out. But usually, with this sort of thing, the truth remains buried.
FWIW, Mueller's report is not automatically public. Only his indictments are. His finding are "secret," given only to Rosenstein. Political and judgment call from there to share with Congress, part of Congress, the public, etc.
Ok, but I guess I’ll boil it down to this:
Comey TESTIFIED that he leaked info to his friend IN ORDER to get a Special Counsel appointed. That isn’t media/whatever spin. It was his sworn testimony.
Given that, why is a personal friend of his, Mueller, THE Special Counsel? Why not someone without any conflict of interest?