Whats specifically wrong with that? Caching issues?
* 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.
The complexity of dealing with headers seems easier than the complexity of routing constantly changing urls.
How often are your APIs changing incompatibly anyway?
When they do changing the URL should dwarf next to changing the surrounding code to the new data model. If that's not the case then what was the point of the upgrade?