How do you know he is blind to the World Government's horrors?
He's been in the Marines for around a year at most. The man already fucked them over hard multiple times now. Oda has already implied that Fujitora has an anti-WG mindset.
He refused the orders given by the World Government, and instead told his underling Vice-Admiral to follow what he himself deems to be the best course of action.
He publicly told the people of Dressrosa and King Riku that the one responsible for all the shit that happened to the Dressrosa is none other than the World Government itself. In his eyes the Warlords of the Seas were one of the "corrupt" things about the World Government that you're talking about. It's not like the Warlords were an entity on their own, they were part of the World Government's forces.
Capitalizing it all up with this his apology where he spoke on behalf of the Government. Do you think the Gorosei or AKainu or Kong would've done this shit? No, because the World Government is never wrong. Fujitora purposely let things play out so he could expose some of the World Government's corruption. And in the end embarrass them with one of their admirals apologizing openly.
So no Fujitora is not blind to the World Government's other horrors, however, the Warlords were simply a major corruption of the World Government that he needed to get rid of first. As you can't take on "criminals" while being allied with them and letting them take over countries. We don't know what Fujitora's plans regarding the Government are now, but based on Oda's anti-WG thing with him & GB, it's certain that he won't stop at just the Warlords, but work on exposing or correcting the other fuck ups done by the World Government.
Unlike Dragon who seeks to bring change from the outside by directly rivaling the Celestial Dragons. Fujitora seeks to bring a change by changing the Marines and World government from within.