I'm confused. Why would you offload it if you thought it was a good investment?

Massively not an expert, but at that level, things are not a binary "good/bad investment". Financial institutions have policies regarding finely sliced debt types, ratios, risks, lengths, sectors, etc.

I personally think it's all hugely overcomplicating things but that's the way modern world works.

(until it every now and then, on regular intervals, doesn't:)

The short answer is to free up money to make other investments.

The longer answer is that banks generally have policies about how concentrated they can be in individual borrowers, industry sectors, geographies, etc. That is why you rarely see a single bank take all of a very large corporate loan. They syndicate it out.

Banks like good investments, but they like being paid fees more

They make money as middlemen, not the ultimate holders of debt.