Ignoring 3xx responses for a moment, I wonder why the HTTP location header is only used in conjunction with POST requests/201 (Created) responses.
From the RFC 2616 spec:
For 201 (Created) responses, the Location is that of the new resource which was created by the request.
This is a widely supported behavior, but why shouldn't it be used with other HTTP methods? Take the JSON API spec as an example:
It defines a self referencing link for the current resource inside the JSON payload (not uncommon for RESTful APIs). This link is included in every payload. The spec says that you MUST include an HTTP location header, if you create a new document via POST and that the value is the same as the self referencing link in the payload, but this is ONLY needed for POST. Why bother with a custom format for a self referencing link, if you could just use the HTTP location header?
Note: This isn't specific to JSON API. It's the same for HAL, JSON Hyper-Schema or other standards.
Note 2: It isn't even specific to the HTTP location header as it is the same with the HTTP link header. As you can see the JSON API, HAL and JSON Hyper-Schema not only define conventions for self referencing links, but also to express information about related resources or possible actions for a resource. But it seems that they all could just use the HTTP link header. (They could even put the self referencing link into the HTTP link header, if they don't want to use the HTTP location header.)
I don't want to rant, it just seems to be some sort of "reinventing the wheel". It also seems to be very limiting: if you would just use HTTP location/link header, it doesn't matter if you ask for JSON, XML or whatever in your HTTP accept header and you would get useful meta-information about your resource on a HEAD request, which wouldn't contain the links if you would use JSON API, HAL or JSON Hyper-Schema.