Why are they paying $3000 per book. Does anyone think these authors srll their books for that amount?

Copies of these books are for sale for much less than that - very very few books demand a price that high.

They're paying much more than the actual damages because US copyright law comes with statutory damages for infringement of registered works on top of actual damages, between $200 and $150,000 per work. And the two sides negotiated this as a fair settlement to reduce the risk of an unfavourable outcome.

If you acquire something illegally of course the judgement against you has to be much higher than the legal price. Why would anyone purchase anything if the worst thing that could happen to you for stealing it was just paying the retail price?

They are not paying for reading the book, they are paying for redistributing the book in perpetuity presumably.

Nope, the settlement specifically excludes actions after Aug 25th 2025 (not perpetuity), and it specifically excludes the output of LLMs (not one form of redistribution).

Meanwhile it's not alleged that they redistributed the books in any form except as the output of LLMs (not any other form of redistribution).

This looks to be almost entirely a settlement for pirating the books. It does also cover the act of training the LLMs on the books, but since the district court already found that to be fair use it's unlikely to have been a major factor in the amount.