I think using the siteaccess configuration is not a good solution and it will confuse website owners / administrators. This widget should only be based on the user rights.
Based on the design we have for the widget, we should fetch the content types based on the language selected in the dropdown list.
||Blog Post (english)
When an editor (having the previous rights) will click on the create button, the editor will see only Blog Post because English is pre-selected. As soon as the editor changes the language to french, the list of available Content Types changes and displays only Article.
This is only an example. And there is more regarding user permissions on content/create: sections, location, subtree, parent...
If it's not possible to do that today because we need to improve/rework the API we can create a story for that.