If the mortgage is in your name and you charge them rent, you don't co-own the house, you're a landlord that's gaslighting your "friends" and probably getting free maintenance and labor to boot.

Everyone would be on the mortgage if the goal wasn't to exploit them to build your own equity.

Do you exploit them less than others would? Possibly. Or maybe not depending on circumstance. Congratulations on being the last in the line.