Such a coincidence that I was just recently listening to the Persona 5 (then Baccano) soundtrack but that's as close to big band as I get.
While copyright is the main culprit, there are others. Electronic aspects reduce the chance music can be played with your acoustic instrument. Composers like Varese anticipated challenges in reproducibility and instruct their readers to record their own samples so that no two performances will ever be identical. Of course that very action shifts the performer to a more active role: from musician to conductor. The closest I can approach are pieces for prepared piano, such as the music of Franghiz Ali-Zadeh.
The newfound electronic diversity also pushes composers to invent their own notation, such as Ianis Xenakis, George Crumb, and even as far back as Henry Cowell.
Last but not least classical is a highly curated genre. Which contemporary composers will be remembered a century from now? The current contenders are sufficiently popular to swap for their sheet music (the exceptions I mentioned). I have no trouble obtaining the minimalist works of John Adams, Philip Glass etc.
I still blame copyright to a large degree. Copyright enforcement suppresses the sheet music trade which reduces discoverability and renders the entire genre static, preserving the status-quo of established artists. You hear stories of Chopin, Schumann, and Liszt debating and inspiring each other across Victorian drawing rooms. Copyright suppresses the modern equivalent.
Contemporary music notation is unfamiliar and alien due to lack of exposure, which once again is exacerbated by copyright.
As for electronic music, I'd like to imagine that composers are free to share their samples alongside their sheet music - like source code samples to a computer science textbook - but I doubt it.
It's ironic but your video shows how less regulated public meetups are compared to virtual meetups. Show up to a jam session, grab a fake book, and start playing. Totally illegal online though.