As noted in the docs, $location will indeed not work correctly in this case:

The $location service is not able to function properly if the current URL is outside the URL given as the base href.

We could make $location use a different baseHref, but link-rewriting would be broken.

TBH, I am not even sure what the usecase is. Why load AngularJS on a page that doesn't match the intended baseHref?)

The canonical location is /baz/, and any links that people copy should use that location, but sometimes it's served at other locations. Either as an alias for compatibility reasons, or it's an endpoint that's embedded by a third party or at the end of some sort of OAuth or other SSO flow, in which case the server has some extra work to do to validate that request and set context, but the angularjs application is still the same.

If $location will be unable to do its job, it'd be nice if it threw an error telling us that explicitly, though I fear at this point that'd be a backward-incompatible change.

(in practice, the app does otherwise work, and only failed when we added this bit to app.run())

Yeah, changing that would be a breaking change. (We can still consider it for 1.7, but I am not convinced it is worth it (nor that it isn't).)

(in practice, the app does otherwise work, and only failed when we added this bit to app.run())

It might look like it works, but could break in subtle ways (e.g. clicks on links being handled incorrectly). It really depends on what features you depend on, but you are in dangerous waters.

You can obviously work around that, but proceed at your own risk 😁

We are going to post a warning in the console when you try to do this (rather than throwing an error). This will help developers find out why their app might not be working correctly in this case.