The purpose of the debt forgiveness is precisely to transfer wealth to people who need it. Whether the institutions can be profitable or not without further government funding is practically immaterial. If the institution is doing a social good, it probably cannot be self-funding. In which case, yes, we will bail it out again. And again. And essentially just make higher education something that the state uses it's tax revenue to provide for it's constituents because they've decided that that is what they want.
Of course, the rich will pay disproportionately for that. But then, they have benefited disproportionately from living in the society. The institutions that provide "social good" for this small minority are already funding proprieties for the state which panders to their every need and whim. So why shouldn't actually socially beneficial institutions like schools and universities also be funded?
Who could possibly be baffled by this? Nobody, except for multi-millionaire tech-bros.