I didn’t realize Xen migrations were made available from a uniform web API accessible from remote tools and fully abstracted/automated at the cluster level.
You are focused on the details and missing entirely the point of my post.
That's 2001, and Virtuozzo was already advertised supporting migrations.
OpenVZ remained super popular for at least like 10 years after it was open-sourced as OpenVZ in 2005, well into 2015, at least. Primarily because it allowed over-provisioning of RAM and all the other resources, which wasn't possible in other environments without the memory balloon drivers and other issues.
I imagine the major reason OpenVZ has declined in popularity is because nowadays memory is cheap enough that over-provisioning of RAM isn't that much of a selling point, and not being able to run your own kernel with processor-guaranteed virtualisation, is deemed too old-fashioned and less secure for true multitenancy than Linux-KVM, which has basically taken over the entire market, from both Xen and OpenVZ, and VMware, and everybody else. Even Amazon EC2 is based on Linux-KVM now, whereas previously it was based on Xen.