These advantages are in comparison to other forms of virtualization, like VMware or Xen (which your original post did mention.) If you're happy with a single image of Linux, then it's almost all moot. (You might still like, say, migration.)
Many people find they want to supply root-on-a-Linux-box to multiple mutually-untrusting users; VMware, Xen, and OpenVZ are all ways to do that (among other use cases.) Broadly, enterprises seem to like VMware, giant cloud providers Xen, and web hosters with their razor-thin margins like OpenVZ or its commercial version.