The desired functionality is indeed possible, but no mentioned in the docs at the moment. You just have to issue an update request to your content type with the following body:
This request will remove the field "my-field-name" from all items. You can also specify a filter in order to remove the field only from items that match a certain condition (using the X-Everlive-Filter header or the filtering methods in each SDK).
Additionally if you want to have the field completely removed, you have to delete it from your content type structure as well.
Hope this information will help you.
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