And in the meantime, they get to retain the full power and influence that comes with the stock/company that they control. The wealth inequality issue is as much about power dynamics as it is about dollars and cents.
> borrow without collateral
And it would be trivial to write the law to prevent that loophole. If a person has any unrealized gain over a certain amount, then any personal loan, secured or not, would qualify for some sort of realized gain tax.
Personally, I think it is simpler and more elegant to implement a wealth tax. It would encourage the wealthy to take more income or dividends to cover the tax, and it would also help shift investments towards more profitable/cash flow positive ventures. For example, all of the tech unicorns burning loads of VC money to acquire negative cash flow would be penalized under such a scenario.
And a trivial way to work around your proposed rule: borrow without collateral. Why would a lender be willing to do this? Because they know the other party is wealthy, that in the event of bankruptcy they have ways to collect, they make money on interest, and it is tax efficient under your new rule.