Furthermore, I don't see how fixing the income inequality fixes the root problem there.

It doesn't, but it might make the lives of millions of people better in the medium term, and possibly result in knock on legislative changes that give more power to working people: repeal of anti-labour laws and so on. Which makes further real change to the system more likely and possible.

You will find many far left wing types have little interest in proposals to fiddle with the tax system, for the reasons you describe: it doesn't fix the real problem. And in a funny way it may well be against the interests of the proletariat: it prolongs the slow death of the current system. That doesn't mean the far left doesn't talk about income inequality of course, but they do so with a different aim: to increase awareness among the working class of their exploitation, with eventual revolutionary goals.

People have been debating the relative merits of gradual reform/revolutionary change for a long time now…