Is this legitimate? Should the Tolkien Estate even allow such a thing?

It probably is legal, though a complete waste of money, in the same way that you can get books of Wikipedia articles on Amazon.

To my mind the problem is not this book, the issue is that ChatGPT is using copyrighted work to generate this, and I can see a lot of court cases addressing this issue.

As Trotter says, it probably is legal, in fact I would go a little further and say that as long as there is no plagiarism involved then this is legal, and should be.

This is essentially poor scholarship using AI but at no point should the Estate have the power to shut down stuff like this unless it is abusing their property.

I guess it is no different to a David Day book - and these have been selling for years (although at least some of these were approved by the Tolkien Estate according to Wikipedia). The amazing thing is there is virtually no real Tolkien scholarship in the book linked above - it really is just a ChatBot considering Tolkien characters (I read the free excerpt on Amazon).