It does not make pages rank, but it makes sure they are found, and it tells the engine which have changed. On a site with more than a few dozen pages it is the difference between a new page being indexed in days and in months.
The date matters more than most people think. If lastmod is stamped with the build time on every page, Google learns the signal is meaningless and stops trusting it for the whole site. A sitemap should carry the real date the content changed, and nothing else.