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Let's say we eliminate all billionaires and confiscate their entire net worth. That gives us a pool of $13.6 trillion dollars. Now in reality you could never do this since net worth doesn't transfer directly into liquid cash and if you made Jeff Bezo sell off his $90 billion worth of amazon stock all at once you wouldn't get $90 billion for it, but let's just pretend. 
So let's take that $13.6 trillion and equally distribute it among the world population. That's $1700 a person. In the US that's less money per person than the total of what was given out by the government in the form of Covid stimulus. 
Does this solve inequality? Obviously not. In America $1700 isn't going to make a dent in income inequality because you still have some people making 20k a year while others are making 80k and a one time injection of $1700 isn't going to change that. So if eliminating all billionaires and redistributing their wealth doesn't solve income inequality then Billionaires are not the cause. 
The problem has a lot more to do with concentration of resources in specific countries. The bottom quartile in America live downright lavish lives compared to a Vietnamese subsistence farmer or a Guatemalan factory worker. While the subsistence farmer breaks his back 12 hours a day 7 days a week farming just enough food to get by and lives a life of hunger and malnourishment, food is so plentiful and cheap in America that for the first time in human history being overweight is correlated with being poor. American household hold over $98 trillion in wealth while only $5 trillion of that belongs to billionaires. America as a whole makes up only 4% of the world population but holds 25% of the worlds wealth.
Yesterday was CEO jackpot day in Belgium.  Yesterday CEOs of a BEL-20 company made as much as the average Belgian does in a year src.  While CEOs might not be te biggest sources of inequality if you compare them to billionaires they most certainly contribute to it. >

Billionaires are bad because they own the means of production and exploit the labour of everyone that works for them to a much greater extent than others. CEOs aren’t as bad, but they still exploit their employees and their class interests align with billionaires in maintaining private ownership over the means of production. 
If a working class revolution was ever a realistic possibility, most CEOs would be on the side of capitalism against the working class. They have too much to lose. >


when the real inequalities are due to existence of billionaires

This is wrong. Billionaires usually start with an idea. The result of the success of that idea is increasing the total wealth. They get a large cut of that increase.
Think of the major inventions and how they made us better off. 
It's a misconception to believe that wealth was and always has been a pie and that if someone gets more everyone else gets less.
I'm deciding to make this short because i don't feel like writing too much but that's the simple way to put it. >

Most CEOs of large companies. A company worth $100mil isn't paying its CEO 9 figures annually >


A company worth $100mil isn't paying its CEO 9 figures annually

No they aren't, but they do pay them with stock.  Famously, Bezos only took $85k as a salary from Amazon. >

I'm taking about total compensation, obviously >

inequality is due to money, not the owners. there is no world where the capital stabilizes all of the beholders on equal ground >

While that's a good statement to make, in current scenario, it's like saying that high murder rates in Mexico isn't due to the gangs but due to guns >

The high murder rates in Mexico aren't due to gangs or guns, those are the symptoms, not the cause. The cause are political realities that encourage violence as an effective strategy for managing narcotics distribution, mostly the demand for drugs in the united states. If you could snap your fingers and replace every single person in mexico with people from say... finland with no other changes, you'd end up with the same drug violence after a short period of time, because people are largely the same everywhere. Systems are the only thing that really differs.
Same goes for billionaires. They exist and are harmful because the economic system we live in allows them to. They're not uniquely bad people who just so happened to have a lot of money, and if only some other people had all that money things would be better. They're a symptom of the problem of economic policy not checking the natural tendencies of capital in a free market to flow towards an ever increasingly small number of people. I'm not saying you're wrong and that CEOs really are responsible for income inequality, but that no one group of people is. The systems we choose to put in place are to blame. >

Definitely, the system we have is one of the reasons for billionaires to exist and I'm not saying they are necessarily bad people but they are often disconnected from ground realities and don't have empathy for the masses. Kinda how people will dehumanize someone with 10X less income than us. >

You should focus on the vehicles that make loopholes against wealth gathering such as Trusts and Board seats >

Wealth gathering only exists because private property exists. Trusts and board seats have nothing to do with it. >

The vast majority of your list of billionaire tax breaks are not remotely exclusive to billionaires. They are just bigger numbers for similar things that other far less wealthy people use, especially CEOs. >

The framing of this is a little difficult because they aren't a 1:1 comparison. 
Billionaires certainly play a role in the passive accumulation of wealth. And I'm using passive to mean, they are allocating capital, lobbying for privilege and deploy indirect power in our economy. However this is generally private, away from the public. 
CEOs are the public faces of institutions that absorb our incomes via the market and return some % of that value back to consumers via labour. Businesses are the vehicles billionaires use to extract wealth from the population. 
It's very obvious why the public heavily focuses on the institution they have deal with face to face, for the vast majority of their lives. Marketing even reminds us they exist. Billionaires are a tiny group that are surrounded by privacy and security. I couldn't locate a billionaire if I tried but I could easily find a bank. 
The public are angry at the highly visible vehicle of wealth inequality rather than the beneficiaries of wealth inequality that are purposely hidden.