Well, there would still be a basis for some interest, because the lender could make more money on their capital by using it for another purpose, such as buying

Well, there would still be a basis for some interest, because the lender could make more money on their capital by using it for another purpose, such as buying T-bills or some other security with essentially zero risk. Intuitively I'd think that part of the interest charged on a loan is literally just to "rent the money", preventing it from being used for another purpose; the rest is to account for the possibility that the loan might not be repaid.