> reinvesting that into the stock market
Yes! Certain classes of loans against securities (e.g. pledged asset line[0]) cannot be used to buy more securities. Margin loans, on the other hand, can be reinvested to add leverage, but come with higher interest, more regulations, limits on borrowing relative to equity, etc.
Of course, like many things, the Very Rich can get around some of those limits viz. Bill Hwang doing (apparently) very much what you describe.