Bug: adding new contact through relationship limited to subtype
I just replicated this.

First, let's discuss the workaround:  Go to Administer menu > Customize Data and Screens > Profiles.  Click on "Reserved Profiles" and edit the "New Individual" profile.  Add the "contact subtype" field and save.  Now, when creating on-the-fly individuals, you can select their contact subtype.  I tested and confirmed that this works.

As for the original problem, I agree that this should probably be considered a bug.  However, given that this is a relatively infrequently-used workflow with an easy workaround, I doubt the core team will be investing resources into its fix.  I'm sure they'd welcome a patch though.