It's the pigeonhole principle; there are only a few long videos possibly encodable as short programs because there are only a few short programs in the first place. To get compression performance, one has to target an ever smaller subset of possible videos, which eventually starts becoming an AI-complete problem.
Is it really? Could a human meaningfully distinguish between 2^4096 different 4 minute videos?
A five-word sentence with 1000 options per word isn't 5^1000 but only 1000^5 = 10^15. If we break the movie into 5-second blocks we get 48 of them in a 4-minute movie so (10^15)^48 = 10^720 different movies, which is not bad but we're still 10^513 away. There are a lot more variations we could consider - different actors, costumes, sets, framing, color grading etc. and I think it's plausible that we could come up with enough features. Heck if you talk twice as fast, you could get (10^15)^(48*2) = 10^1440. But it's a lot bigger than I made it out to be.
Although disappointing, you seem to have the correct answer for my question.
The only thing I have to give this function, is the height/width ratio, some other ratio that define how large "corner holes" are in the LST configuration, the amount and relative position of windows and door, the starting point and NSEW direction for inside walls, and with all that, I could create a house of a story building with an inside. Of course it's not finished yet, and there isn't furniture of details, but you see that in theory, you can use procedural generation as a compression tool for human-designed structures, that no machine learning algorithm or autoencoder could really achieve.
If you associate this kind of algorithm into a well made openstreetmap database (think vector tiles which are used for GPS software), you could also recreate the whole world in 3D, with enough details to make a game that would not require that much disk memory. Recreating the roads, fences, parks, rivers, vegetation, elevation etc is difficult because it require a lot of tuning and geometry tricks, but it's very cheap in term of cpu cycle and disk.
The folks at outerra have begun making an actual software that lets you browse the entire planet in 3D. You can zoom in real time from space to 1cm. They don't have cities yet though, but they are planning for it. I want to make a game using such ambitious ideas, but it's not easy...