Here’s another review from Maureen Mann

https://scholar.valpo.edu/journaloftol ... Ses2jA-m735wCQLgx7Y1gVZVs

Abstract:

This essay review interrogates the polemical style of rhetoric in Holly Ordway’s Tolkien’s Modern Reading. It critiques her use of a fictional narrative to represent an adolescent Tolkien, her intertextual criteria, and her dating of Victorian fantasists and their historical moment. It questions her claims about entrenched notions concerning Tolkien, her use of evidence, and her assumptions about her audience. It concludes that Ordway is less interested in Tolkien’s contemporary reading and more interested in creating a new narrative about Tolkien the author.

"largely [Ordway] is interested in showing what Tolkien read but not necessarily how such reading might have influenced him" — well, yeah! Hence the title. So what? Does Ordway anywhere claim influence from all of Tolkien's modern reading? If not, what's the point of this statement?

I personally feel that the reviewer addresses your point, in context.

By the time Ordway reaches truly modern authors in Chapter 10, she has largely given up even on homage; she identifies some of the twentieth century authors Tolkien read (Dylan Thomas, Agatha Christie, Roy Campbell, Osbert Sitwell, Edith Somerville, A Neil Lyons, Stephen Spender, George Stein, Saki) only by listing them. For these writers she does not show they have any influence on the Middle-earth works or Tolkien’s creative imagination; she has no textual similarities to show, or even simply similar events or themes, or how Tolkien transformed these works for his artistic vision. It is just a quick survey. She does examine other writers in more detail, but largely she is interested in showing what Tolkien read but not necessarily how such reading might have influenced him, if at all. It is, of course, her choice to write the book she wants and not the kind of book most common in critical literary studies.

I don’t think it needs to be taken as a negative for a book review to state some obvious things - the reviewer read the book, and others haven’t yet, so saying what the book does and does not do can be useful to many.