I believe that the "Add" functionality really does need to be enhanced to ensure that users are adding child Features under a parent in a way that fully acknowledges the context in which those children are being added (and field requirements are a totally valid type of local context that really needs to be honored in the Quick Add functionality.)

I personally believe that this feels more like a bug than it does a suggestion since I believe that users would both expect local context to be honored while also being surprised/disappointed to discover that local context is not being fully honored via the Quick Add.

But regardless of the bug/suggestion question, I very much believe that any deficiencies perceived by users related to parent-child relationships and creation of work items is a high-priority to address given the activity volume of how many times per day the average JA users needs to create parents/create children/create relationships between parents and children.

(3527dd023282: I definitely agree that the ability to disable the Quick Add function is a fair workaround and probably worth giving admins that ability anyway for several reasons.)

3527dd023282 , I do understand the added functionality of the Quick Add and the fact that is a handy feature. But in our opinion all mandatory fields should at least always be incorporated in the fields to be populated. Or there should be a check when opening it later, so the data quality issue can not exist for long. Indeed disabling the quick add functionality is also completely fine as product enhancement. 

Stating that just training not to use it and expecting that no one of the thousands of users will try this function which is so clearly available and use it  - and tell others it's more handy and so on and so forth - will not work I'm afraid. 

The behavior described is part of the Quick Add feature to be able to setup new Story/Features without having to populate all fields.  Suggest training your users to not use that functionality to be sure you don't hit this condition.

Another valid product enhancement request could also be to be able to disable this Quick Add functionality.

We cannot have a bug created when something works as designed, but we really think this should be one based on a design flaw. 
The 'Add' functionality makes it possible to have features without the required fields filled. As long as the feature itself is not changed this can remain, even when child items, links etc are created on this feature. And thus creating a significant data quality issue within our company. That can never be the meaning when it was designed in our opinion.