The family can make any agreements among its members, but remember that lenders aren’t part of those agreements. If the parents want to pay the loans taken out by the student, great. If the parent dies or decides not to pay, the student must pay the loans taken in his own name. If the student agrees to pay the Parent Plus loans, the parents are trusting that that will happen, but the lender won’t care. It expects to get a payment from the parent every month.
Also, the loans cannot be combined so there would be 2 payments if either the parent or student is paying the other’s loans, and the loans taken by the parents wouldn’t be eligible for IBR based on the student’s income.