Ajax tends to operate outside the normal web viewing experience. Usually, you click a link to a page, your browser opens another page, you click another link to another page, it's loaded into the browser, and so on. If you wanted to return to the original page, you would click the Back button, navigating back through all the pages visited in the current session. If you wanted to bookmark a page or create a link to the page, you would just copy the URL that's loaded in the browser's navigation bar.
Lack of real web paging is also a big issue for much of a site's advertising. Before Ajax, ad costs were based on the number of page views for a site. Now, if content can be loaded willy-nilly into any page that opens, page views no longer reflect what's really going on with a site.
Search engine optimization also takes a ...