Harry's failing pretty badly to update sufficiently on available evidence. He already knows that there are a lot of aspects of magic that seemed nonsensical to him: McGonagall turning into a cat, the way broomsticks work, etc. Harry's dominant hypothesis about this is that magic was intelligently designed (by the Atlanteans?) and so he should expect magic to work the way neurotypical humans expect it to work, not the way he expects it to work.

I disagree. It seems to me that individual spells and magical items work in the way neurotypical humans expect them to work. However, I don't think that we have any evidence that the process of creating new magic or making magical discoveries works in an intuitive way.

Consider by analogy the Internet. It's not surprising that there exist sites such as Facebook which are really well designed and easy to use for humans, rendering in pretty colors instead of being plain HTML. However, these websites were created painstakingly by experts dealing with irritating low level stuff. It would be surprising that the same website had a surpassingly brilliant data storage system as well as an ingenius algorithm for something else.