However, just as with POST requests, it might make sense for the server to respond with a redirect to a URL that could be shared.
That said you should be able to trigger any custom HTTP request your browser support via pasting/bookmarking a `data:` or `javascript:` construction if you really want. As of now the URL bar is GET only when you enter a URL.
Just as a small remark, HTTP protocol standards do - or have at least - considered URL input so far in a wider, client-side meaning. Some details are left for the clients, e.g. it differs across browsers how certain URL characters are interpreted when entered into the URL bar (or on the command-line, e.g. with curl(1)).
Apart from that, HTTP URLs are part of the same HTTP standard, aren't they?