Yes, but then they could also select a video that was uploaded to the gallery section, so that wouldn’t work either. Also the hook option would not be very user friendly, as it first suggests you could upload a video and then after you have done it, it “kicks it out of the field again”.
What would solve this issue altogether would be, if file sections allowed to hold several types of templates, not just one. That would also additionally solve the other issue, I had a few days ago.
Would this (sections with more than one template) be a reasonable feature request? If so, I would write one up on GitHub. Would make some scenarios easier for me at least.