In all fairness, private investment was much lower when this was the case. Companies used to do an IPO much earlier when they needed funding instead of raising hundreds of millions in private investment money.
It's unfortunate that this doesn't make sense to you, because that it literally the original purpose of shares in a company.
Someone wants to finance a voyage to a far-off land to trade. To do so, they form a company and issue shares of the company. The profits off the voyage (if any) are then divided amongst the shareholders, in proportion to shares held. It was a pretty good idea.
(Debt is not the same as equity, not sure why you are talking about mortgages).