It is a thorny question. The best way I can square the difference is that generally buying a house with debt is on the debtor and the house itself is collateral. The debtor can't pay back the loan the house is taken by the bank to be sold. Where as a PE leveraged by out the debtor is the target company. A company is different than real estate in that they are a legal entity that is now responsible to pay back a loan equal to their own value. The collateral is the business, but the business is now illiquid and has to sell of real assets and go bankrupt.
For example, Joanne's Fabrics was a profitable business with a fair amount of real estate. After PE bought them and was saddled with unreasonable debt they were in the red and had to sell all their stores. This removed useful and profitable business from the economy and sold off the assets in a fire sale. Where as me losing a house just means a bank now owns it and someone else can buy it. But if someone were to buy Joanne's they'd have to pay off the debt Joanne's owed for being bought and run into the ground
There is a long practice of having cosigners on home loans. This feels basically like that.
Which, granted, if you don't like the idea of establishing a company to take on loan responsibilities, I am not trying to offer a defense of that. Was a legit question of how you would structure it so that this is illegal, but home/auto loans are not.