Private Credit & Interest Tax Shields?

Curious on how interest tax shields would work if a private credit arm of a PE firm finances an LBO by that PE firm.

So let's say KKR Credit provides a loan to KKR in its buyout of company XYZ. Interest expense paid would go to KKR Credit, net income of the portco would go down, but total value to KKR (for PE+PC) is higher than if they were financed by a bank. Portco (and subsequently the sponsor) gets tax deductible from interest paid, and credit arm gets cash flow from the interest expense. Isn't this a win/win for PC and PE at the firm?

Not sure if I've got all that right, but just curious on how much this happens. How often are private credit arms financing their firm's buyouts?