Capital gains taxes (paid by shareholders) are completely separate from corporate income taxes (paid by corporations). You're also forgetting (or ignoring) that the legal incidence of a tax and the economic incidence are completely separate. For example, employers and employees are both legally responsible for paying a portion of payroll taxes, but economically speaking that tends to lead to lower wages, making the employer's portion fall at least partially on the employee.
I'm a bit confused by your post, it seems you are agreeing with me, but you say you disagree?
I am aware of the difference between capital gains tax and corporate tax (also note that not every country has a capital gains tax). My argument applies to both, i.e. one of the reasons for raising inequality is the inbalance of labour and capital and the low corporate and capital gains taxes definitely contribute.
About the effect of income tax on salar, I'm not quite sure what that has to do with my points. I was not arguing that we should eliminate corporate tax and just let income tax handle it. Unless your argument is we should use income tax instead of corporate tax because it lowers salary?
Yes - corporate income tax should be eliminated entirely - the revenue can be made up in other, less terrible ways. Corporate incomes taxes are a poor way to address inequality because they tend to fall, at least in part, on workers, and not on wealthy people themselves, who largely accrue wealth through investment, not work. If the goal is to reduce inequality then we should simply tax rich people more, not corporations, whose money will eventually be passed to shareholders anyway.
https://voxeu.org/article/effects-employer-payroll-tax-cuts