the usage being described is 1 physical copy = 1 streaming, thus if you cut it to 10 second clips only 1 particular 10 second clip could be streaming to any one customer at any time to match this model. Thus you still end up with 1 physical copy = 1 streaming. It is illegal but shouldn't be, because of first sale doctrine being a match for this use case. I can only show you the first 10 seconds of the film if nobody else is watching it.
I see that what you're saying is that User X could watch the first 10 seconds and then the second 10 seconds while you start you're first 10 seconds but that would be sort of a ridiculous use case for the following reasons:
1. your system would include a bunch of extra work for your solution to make this work, easier and cheaper to buy 10,000 copies of the movie and stream as needed.
2. people pause movies thus your solution becomes even more expensive because it would need to calculate out who has paused their ten seconds at the 5 second mark etc. etc.
Thus it seems likely that any solution being built on the model of we have physical copy we stream you copy will be built with showing complete movie and not any clever cutting up of movie to make the number of physical copies we have stretch further. The way the law works each different use case - cutting up movie, showing complete movie - would probably be challenged and there is no reason to suppose that they would all be allowed to pass, in fact since the showing complete movie was not allowed to pass in the real world it seems unlikely that the weird edge case cutting up movie would be allowed to pass even if law was changed to allow showing complete movie was changed.