Prosper on the other hand could send disbursements directly to the creditors FBO the borrower.
They could. However, I think there are several problems with this. First, if the original debt is a credit card, the guy can just charge more stuff on the credit card, and take his balance right back up. What would P have accomplished?
Second, I think for a consumer loan of some sort, forcing the borrower to give up all the information about his other loan (or loanS), contact info for the company, loan number, balance, etc, would be a big hassle, and would deter borrowers. P and LC have streamlined their web sites to make things as simple as possible for borrowers, so as many as possible will complete the process. This is important because borrower acquisition costs are significant, and borrower completion rates limit the business. You don't want to waste them once they come to the web site, so you keep things ultra-simple. The more web clicks you demand, the smaller fraction of folks complete their loan applications.
Also, even when the guy does complete all these new fields, sometimes he will have made an error, and you have to sort that out, which is increased administrative burden.
In the end, I don't think it would be a win for P, and that's why they don't do it.