Cannot set default text/profile format if no default text is provided

I have different long text fields on the same content type.
I want to use different CKEditor profiles, for example:

one text field with a "Basic" profile, which is a plain text format modified to allow some html tags
one text field with a "Basic + images" profile, which is a modified filtered html to allow img tags (the CKeditor profile is configured to use the Media module plugin for inline images)

The CKEditor profiles are tested individually and working well, but the problem is that I cannot set a default to show them on the corresponding fields once on the node add/edit form. I don't want the user to select the text format from under the text area (I will hide that with CSS), but rather use the one I configured as default for the field.

The CKeditor instead will always show the profile of the first text format (weight configured in core at admin/config/content/formats) even if at field settings I selected the second one for the default, otherwise I actually write some text as default value for the field (obviously not something you want to do because you will actually create some content on all nodes that have that field empty).

This is weird, and could possibly be a Drupal core bug but.. can you investigate please?