You could argue that capital gains rates are too low, but that's a different argument than saying stock owners are getting "invisible income".
The above assumes you control the shares and they are pledgeable as collateral. It is not easy, but doable, to borrow against RSU's. i.e. you probably need a high net worth/private banker relationship.
You're right however, if you want to acquire more shares using margin, then your equity needs to be at least 50% of the stock value, i.e. with $10k you can purchase (up to) $20k worth of stock.
You can't put $10K into the account, buy $10K in shares, and borrow $10K in cash (leaving 0 net equity in the account).
Your scenario where you can borrow 100% of the value applies only if you apply that 100% to further shares (meaning you buy 2x as many shares and have a margin balance of 100% of your original equity but 50% of the shares' value).
That means you can buy $20K worth of stock using $10K of cash.
There is a separate, lower limit called the "maintenance margin" limit, which is the equity percentage that you need to hold to avoid a margin call on a held position.
So, if you deposit $10K in shares, they appreciate to $12K, you borrow $6K and then the share price falls back to the original amount, you have $10K in shares, $4K in net equity (40%), but are probably not going to receive a margin call.
Or, if they are worth $10K, you borrow the limit of $5K and the share price falls by 1%, you won't get a margin call there either (on most securities).
Otherwise its just a collateral.
You might not want to sell shares that you've held 306 days, preferring to hold them an additional 2 months to get long-term capital gains treatment on them.
You might not want to take capital gains (even if long-term) on this year's income tax. Maybe you want to defer it to January; maybe you want to defer it to a later year when you expect to have a lower capital gains bracket or when you expect to be able to avoid the Obamacare surtax on investment income (via repeal or via lower AGI)
You might not want to sell shares if the margin loan rate is lower than your expectation for growth of the shares.
And you have to do it yourself!
When a bank borrow you money they don't actually take it from somewhere they fundamentally can create it because of quantitative easing pushed by central banks.
The digital monetary system today is a far cry from the gold based system and the ability to use money as if they are income are very real. Money is more a concept today.
They can't do it without the Central Bank and it's the same mechanism as allows for QE. It's only possible in a FIAT based system.
When banks do it it's called fractional reserve banking but the mechanism is fundamentally the same, the ability to "create money".
There's no mandate that bank notes need to be issued by a central bank. See the article: https://en.wikipedia.org/wiki/Banknote
So yes it requires a central bank as it's through them the recognition happens. Philosophically all money requires is trust no matter what not even a legal entity as long as people trust it, but practically to claim that central banks aren't needed for FRB is wrong to the best of my knowledge.