If only things were that simple. A demo video can show that there is an interaction that doesn't stutter, not that there is no interaction that stutters.
I realize it's imperfect, but it would raise confidence to see a video of something that looks fairly consistent with the advertised usage that satisfies the benchmarks.
The video doesn't guarantee bug-free play, but it can give us confidence that the benchmarks are an honest test since we can see what the test looked like.
If it's a text editor and it just shows that opening a new blank file and typing a few words is fast, or a game that shows the game runs well in an empty room level, then we know the demo is dishonest. And having a "boring" video in their store page won't win them much buyers. You want all the ad content to look as good as possible, so the demo video would be best if it shows off the most impressive features of your application, which is where we'd expect performance problems.
That said, it's probably not feasible because creating a full benchmark script that also doubles as a real-world demo for an app would be too much burden to put on developers.
So right there on the store website is the "demo video".