If a journalist or concert promoter calls you and asks for photos, your biography and quotes in a hurry, having a press kit prepared in advance enables you to respond quickly and efficiently to that request. Rather than searching your hard drive for saved emails and copying and pasting reviews into a document, your press kit is already formatted, organized and ready for you to distribute.
Keeping everything pertinent to your band, to use that example, in a single file reduces the risk of mistakes. For example, last year your band did a photo shoot. Your drummer quit the band shortly after, making those photos out of date. These photos may still be online, so a journalist could use them in a review. If you send out an EPK, then the journalist won't be tempted to use online images since you have preselected photos included in the press kit.
The purpose of a press kit is to make the life of journalists easier. If a journalist has space to write about one band, and she likes two bands, then with everything else being equal, the chances that she'll write about the band with a solid press kit is higher. The press kit reduces the need for her to gather photos, biographies and upcoming dates. The journalist wants to spend time writing about your act, not researching the names of the band members. A press kit won't guarantee you a review on an influential blog, but not having one will diminish the chances.
Because you prepared the press kit, you control what is in it. This reduces but doesn't eliminate the chance of your using unwanted information. For example, the last review you received got the bass player's name wrong. If you sent a list of links to reviews to a journalist, then the journalist will see that mistake and repeat it. If you sent over a press kit with only clippings that you want people to see, then most likely they will read that information.