I have reported before on the claims that the billable hour is dead or dying, always adding my opinion that reports of this death have been greatly exaggerated. For my previous coverage on this subject see here, here, here and here. You can also use the search function on the right side panel to look for posts on "flat fees" which discuss how the confusion on how to regulate the use of flat fees in some jurisdictions has eliminated their usefulness as alternatives to hourly fees.
Many of the sources of information cited in those older links come from the Wall Street Journal, which is why interestingly, today the WSJ law blog is finally accepting my view in a short article (available here) in which it states that "[d]espite all the hoopla about hourly billing going the way of the Edsel,
law firms and their corporate clients have been much slower to adopt
alternative billing arrangements than many had predicted..."