Can wealth gap be reduced by not allowing assets to be used as collateral unless they are taxed?

Hello everyone,

I know basically nothing about economics, but I am starting to learn. The state of the world and having some free time triggered this learning.

One of the most common and accepted sentiments is that the rich will get richer and the poor will get poorer. This is then followed by "tax the rich". Which is then followed by convoluted discussions on capital gains taxes vs wealth taxes. Honestly I haven't learned enough to understand that last bit yet.

One of the things that I recently learned and it doesn't seem talked about enough is the borrowing money against assets to buy more assets. To me it seems that this is what all rich people do. And this is where it doesn't make sense anymore.

If I have $1bn worth of shares in a company, I am not taxed on it until I sell them. This makes sense. However, I can borrow $100mil against those shares and buy another company. And it is easy for me to pay the loan back through the dividends and all.

If my understanding is right, won't we significantly reduce the wealth gap problem by stopping this? If you don't pay taxes on the $1bn shares, then those shares cannot be used as collateral when taking out loans.

I MEAN OBVIOUSLY I AM WRONG. I haven't solved an age old problem after two months of economics learning. But tell me why and how I am wrong.

Thank you.