Can't attach files to a Draft via REST API

If you attempt to POST to this url /rest/api/content/

is a draft id, the REST service returns an error

{
    "statusCode":400,
    "data":
    {
        "authorized":false,
        "valid":true,
        "errors":[]
     },
     "message": "The entity Draft = { id: 884782, type: page, title: null, pageId: 0, pageVersion: 0} is not ContentConvertible or API available"}
}

This makes no sense because a Draft is a ContentEntityObject and it's possible to add an attachment to one through the Java API as well as the Confluence rich text editor.