The thing is that Kentico makes a server request to the MVC app to get the page templates, page builder and so on - and since it is a server request, Kentico does not know that there is some basic authentication required and does not add the credentials to the request headers. This would require for you to somehow authenticate the requests made from Kentico - maybe with some middle layer which would authenticate them or something like that.
We do not have support for this as the Basic authentication is not used that much lately as it is not that difficult to break in. I would rather recommend to secure the environment in other way - claims-based authentication, multi-factor authentication or simply IP filtering on the IIS level.