If PE firm A wants to buy company C using an LBO, it could do so by having C borrow money and then A purchase C, or by creating an entity B that borrows money and then purchases C. Whether B or C owns the debt doesn't change anything meaningful for A, and it's pretty clear that you're allowed to form company B (and really hard to imagine how you'd make that illegal without effects that would be worse than current).
I would prefer that! I'd prefer even more strongly that the debt be owed by someone else entirely, so a default isn't associated with me at all. If you're up for it I'd also prefer to use your credit card number to buy stuff on Amazon. But for whatever reason the law doesn't always seem to follow my preference.
I'm sensitive to your point about restricting formation of new corps. The system can't just be changed randomly without extremely careful thought. And often not even then.