There are some things, like political campaigns, where absolute inequality does matter. One man one vote may be true in theory, but in practice Rupert Murdoch has fat more political sway than anyone on this thread precisely because of his wealth.
Personally I think lower inequality in our society would be a good thing - but also with political influence there are more direct faults/solutions.
In the US those are intertwined:
> The court held 5-4 that the free speech clause of the First Amendment prohibits the government from restricting independent expenditures for political campaigns by corporations, including nonprofit corporations, labor unions, and other associations.
* https://en.wikipedia.org/wiki/Citizens_United_v._FEC
More speech for the rich.
As an absurd example, let's say I made a law that said that people with brown eyes can slap people with blue eyes. In this world, slapping people and eye-colour would be intertwined. This doesn't mean it's inherently a problem with brown eyes, or that eye colour and slapping are inherently intertwined. The obvious fix for this would be to change the rule rather than to change everyone's eye colours.
As in the US wealth and political donations are linked, the initial problem is that those two are linked together. There is nothing inherent that says you need to reduce income inequality to reduce the impact of wealth on politics - i.e. you can reduce the impact by changing legislation so the two aren't intertwined.
edit: If you want to do something politically that would harm my business, I can just silence you, have you jailed, or kill you. No campaign finance necessary. I can sponsor debates about the degree to which you molest children in my newspapers and on my television channels every day.
Hell, the money that goes to campaigns that isn't wasted to party graft just goes back to media owners, anyway. It's like US foreign aid, denominated in store credit at US favored contractors.
Even billionaires and millionaires who dont own media companies have outsized influence. They can fund politicians they prefer to an extent that a rival might not be able to match. They can pay for lobbyists. There are a myriad of ways that dollars turn into votes without a mustachioed man walking around with a bag of money being involved. Mass movements aside the working class isnt out there propping up politicians.
Murdoch's own papers claim credit for election victories. I don't know the exact conversion rate from dollars to votes, but it's absurd to suggest one doesn't exist and that Murdoch's organizations don't know what it is.