I'm not sure what you mean by paid. I don't know precisely the location of student debt, but my assumption is i) the debt holder is the government and ii) the colleges have already been paid (this one seems obvious). In that case there is nothing to be "paid out". The government simply says "you can stop paying us" and stops receiving an annual inbound cash flow from student loans (they did this since the pandemic). You may argue they have to then use debt or taxes to make up that shortfall in annual revenue (I would disagree, but that's ok). If that were true, since the US annual tax revenue is over $4T and the annual revenue from student loans is $70B (in 2019) that represents a reduction in revenue of ~1.75% (assuming the cost of collecting student loan payments is $0, which is unlikely). So in the worst case the government must increase their tax revenue by 1.75% annually to account for the loss of the student loan revenue. Doesn't seem that bad.

There may be debt servicing firms making an income from student loan payments, or student loan refinancing companies, but we could ignore those and say they are ineligible.,

Your assumption i) is wrong. The government does not hold the majority of student loan debt. So, yes, the government needs money in order to make this happen.