Sure it’s possible it was “designed to fail” but not because the wrong method was used but because our current extremist supreme court would have used any excuse to stop it. It was based on the same HEROES Act that Trump’s pause of student loans was based on and the act explicitly says “waive or modify” loans so if Biden’s cancelation was illegal then so was Trump’s pause.
Here is a quote from the DOJ: “The plain text of the HEROES Act authorizes the Secretary to “waive or modify any statutory or regulatory provision applicable to” the federal student loan program, … We conclude that targeting relief towards those individuals who suffered financial hardship because of COVID -19 and who otherwise satisfy the requirements of the Act accords with the Act’s requirement that the waiver or modification “be necessary to ensure that” student loan recipients who are “affected” by a national emergency “are not placed in a worse position financially” with respect to their loans as a result.”