It would be most beneficial to have an admin option in Canvas Studio to turn off the Display Media tab feature globally and leave it up to individual cases to turn it on. Alternatively, once a Studio video has been inserted and the unwanted Media tabs display, there should be an option for the teacher to turn off the tabs. 

Right now, our teachers have to edit pages with embedded Studio videos, delete the video with the unwanted Media Tabs, and reinsert it plus remember to turn off the Display Media Tabs option before re-embedding.