Currently, there's not a streamlined way for features to inherit their goals from initiatives as it requires many automation rules. Recently an enhancement was made to allow features to inherit their goals from the epic. It would be ideal if a similar capability was provided for initiatives so that when the initiative of a feature is set, the goals of the initiative are applied to the feature. Also, if the initiative is already tied to the feature and the initiative's goals change, the feature should be updated accordingly.
This inheritance needs to be applied be looking at all related records, not necessarily just parent/child relationships. In the instance above, there is no schedule nested in between the initiative and feature.