First sentence of your last paragraph is quite problematic, as you’re essentially saying, “I see the evidence, but choose to ignore it because I dislike it.”
It is likely that on a static basis, progressive taxes reduce post-tax inequality. But then they boost pre-tax, leading to another round of calls for more progressive taxes, leading to even more lopsided pre-tax income, and so on.
I don’t care what the benefit is. I write about a specific set of topics, and the benefits of public spending is not one of those topics. There may well be great benefits to revenues raised. Or money may be squandered on useless things. I’m agnostic on that. I’m unsure why money transferred from high-savings individuals to low-savings individuals would be construed as accelerating capital formation when it would seem obviously to do the opposite, hence why virtually all economists assume that higher income taxes reduce investment. There’s huge disagreement about how much, and whether that cost nullifies benefits, but you can’t really be arguing that the net effect on investment is positive; that would assume that a larger share of revenues from high-earners are directed towards investment than they would have directed which, given the actual allocation of public spending, seems very dubious.
The focus on pre-tax is a way of showing what is actually happening in the market. Yes, people care about post-tax, but they also care about pre-tax, because pre-tax determines how their income responds to other financial decisions (i.e. AGI), and also determines how their income responds to future tax changes. All else being equal, most people prefer the lowest possible AGI combined with the highest possible post-tax income. So yes, pre-tax matters.
Obviously, we should look at both: and we should keep in mind that efforts to equalize results (i.e. post-tax inequality) may in fact create a more visible and apparent disparity in income. That this disparity isn’t “real” is only a small comfort if your goal was to equalize incomes.