People are less likely to pay their debts if they think their debts will be sold to someone who will forgive it, so the debt issuer's other non-written-off debts will be harder to collect (since now those people know that they might be able to get out of their debts by waiting and hoping they get sold to a debt-forgiver).

That becomes a problem if debt forgivers become a large percentage of purchasers. It doesn't "only work the first time", it only works as long as you're in a tiny minority, which will likely be forever. The debt issuer won't take notice until the value of their debt starts to drop.

The debt issuer would note that they had to write most of that debt off, so the credit score impact will mean that the same borrower will have a much harder time getting another loan.

Ah, you're interpreting it differently: I took them as saying that you can only buy debt and forgive it once, not that you can only have your debt forgiven once.