If you're going to count leverage in real estate returns, the equivalent comparison is margin in stock market returns. You absolutely can purchase $125K in stocks for $12.5K cash if you're willing to buy them on margin (subject to margin requirements, which are often 50% for retail brokerages but can be as low as 3% for hedge funds etc.) Mortgage and margin loan interest rates are even comparable.
The reason people don't buy stocks on margin is because there is risk entailed: if the stock goes down, you can get a margin call, get your whole position liquidated, and lose everything. There is an analogous event for mortgages: if you fail to make your mortgage payment, the bank takes possession, liquidates your investment, and you lose everything. This risk is often glossed over with mortgages because it's a socially-acceptable way to purchase a house, but it's still there. Many people who did precisely this in 2004-2007 faced exactly this consequence in 2009-2010, and are still digging out from the wreckage of ruined credit, lost downpayments, and a home that was repossessed.
> You absolutely can purchase $125K in stocks for $12.5K cash [...]
This isn't quite right. You can only get 2x leverage on your margin account for overnight holds (i.e. long-term investment.) The maximum leverage federally allowed is 4x, and you have to liquidate half before the end of the trading day (to go back to 2x) otherwise your broker will automatically liquidate half of your position.
If you buy E-mini S&P 500 futures, your effective overnight leverage can be up to 22x. You could put part of your money in short term bonds to avoid such extreme leverage.
There are also 3x leveraged ETFs you can hold overnight.
Of course, this means you aren't directly owning stocks.
The reason people don't buy stocks on margin is because there is risk entailed: if the stock goes down, you can get a margin call, get your whole position liquidated, and lose everything. There is an analogous event for mortgages: if you fail to make your mortgage payment, the bank takes possession, liquidates your investment, and you lose everything. This risk is often glossed over with mortgages because it's a socially-acceptable way to purchase a house, but it's still there. Many people who did precisely this in 2004-2007 faced exactly this consequence in 2009-2010, and are still digging out from the wreckage of ruined credit, lost downpayments, and a home that was repossessed.