One of the downsides of streaming’s cord-cutting era has been how hard it is to stumble on a great movie midway through. You know the joy of which we speak. After a long day at work or school, a moment to unwind turns into discovering one of your favorite flicks, that one you’ve probably seen a hundred times, is playing right now on cable. And wouldn’t you know it, you’ve come across it right at your favorite bit.

Before you know it, you spend the next 90 minutes catching up on a film you already have half committed to memory. It’s a perhaps uniquely dated phenomenon, but a great one for those of us who have entire personal libraries of movies that we may never have seen from beginning to end. I spent years, for example, convinced Con Air started with Nic Cage enunciating, “I said...