The inequality problem is much more complex than "government vs. capitalism." It's more like "the managerial class is taking too much rent." The managerial class includes the higher ranking bureaucratic class in government as well as overpaid corporate executives in public companies.
Basically it seems like the managers in our society figured out they could just give themselves raises and to hell with everything else.
To be clear, I was suggesting something along the lines of "The govt. corridor seems to exist in a different socioeconomic 'universe' than much of the rest of the country, so people who operate in that space may have a very rose-colored view of the impact of the current governance regime." This may be part and parcel with your "managerial class taking too much rent" (The hypocrisy that always made me chuckle was how good the congressional healthcare plans were vs. what they'd subject the rest of us to)
Didn't mean to distill the whole "inequality problem" down to this one fact either, it was just what struck me the most when reading the OP.