Omit certain node types even though user roles have permission

Problem/Motivation

Here's an interesting limitation of the current build (I think!)

We have a content type called machine name: question_response that users in the student role have permission to create.

HOWEVER, we don't want them to be able to simply create one from scratch.
Instead, question_response are created on-the-fly using automation (specifically the an ECA → model) and when that happens, certain fields are pre-populate.

Allowing a creation of the question_response manually serves no useful purpose and should not be possible.

Now, there are some obvious ways to prevent anyone at all from seeing the CT appear in the Type Tray using simple CSS but it seems eminently sensible—and useful I'm sure—in plenty of other similar scenarios to have a simple tick box on the Type Tray vertical section of Content Type Overview page which says something like "Omit from the Tray".

Could that be added as a feature?