Book reviews are only one book promotion possibility, and they're the book promotion strategy least likely to be successful.
It always confuses authors when I tell them that, to get their book into the print media, they must think beyond book reviews. For so many people, book reviews are the only worthwhile reason to approach the print media. Sometimes, authors feel that book reviews are the only reason to even approach the media. No book reviews, no happiness. It's even tougher when authors have their hearts set on a particular publication's book review editor and, even after garnering other book reviews, come back and say, "I simply don't understand why publication A didn't review my book. Did you remember to contact the book editor there, or did you drop the ball? Would it be worthwhile if I contact the book editor myself?"
And it's hard to convince these authors that book reviewers usually say "no" to books. They have to. They have a lot of books on their desks, and it's their job to select a handful of books to review or to assign for review. It is not their job to review every book that is sent to them.
There are tricks to finding book promotion opportunities in the print media beyond trying to garner book reviews. You can pitch yourself as an expert to beat editors. You can write an article and pitch it to the editor, and ask that the attribution include your book title. You can also write an op-ed piece and submit it with the same request.
And, certainly, do approach book review editors while bearing in mind that many of them cannot review books that have already been published. If you have the lead time that the larger publications require, and perhaps if you have available advance reader copies or galleys, then sure -- send them off to book review editors, and hope for the best.
But expect to continue your book promotion efforts long after the window of opportunity to get book reviews has closed. There are so many ways to go after book promotion in newspapers and magazines ... keep an open mind to all of them, and don't focus all of your energies on book reviewers who might just be the most overwhelmed employees at the publications that matter most to you.