How rare is it finding a used PSP for $40?

You're making a broken assumption that you're previous $40 purchase for a used PSP wasn't a fluke of a single past seller of the device (which may not happen again anytime soon). Plus you failed to mention how many months or years ago that purchase was. Inflation still exists.

And you're failing to acknowledge that we're in the middle of 2021 Christmas shopping season and given the global supply chain shortage on computer chips and gaming consoles, that people are alternatively also looking to snatch up these retro/used gaming platforms (portable or otherwise) and thusly causing the general market price skyward.

On eBay they have them ...have you looked there?

Unfortunately the price range I've been looking for is only people selling parts only PSP's

It was actually only back in June and it was really used which is probably why it broke easily