Putting the version in a header looks "elegant" at first, as it keeps one URL for one resource. But in reality it adds accidental annoyance with no benefits over having the version somewhere in the URL.

* Have to set up response headers and caching carefully to make sure different versions are cached separately.

* A bit of extra complexity to set up load balancing.

* A bit of extra complexity to set up web framework routing to controllers.

* A bit of extra complexity for logging to track which endpoints were called.

* Calling the URL without specifying a version gets you some undefined version...

* ... or if you require a version header, can't preview GET endpoints in a standard browser.

* If different parts of the API have different latest versions, you can't encode it in an URL and therefore can't return URLs for linking between resources.

* On major version changes you might be removing, renaming or moving URLs, so why keep them pure and versionless in the first place.