This “feature” accomplishes nothing of value for anyone, including the streaming services, but imposes a massive (and for most people, confusing and frustrating) hindrance on honest people simply trying to easily capture high-quality (as opposed to, say, using their damn phone to take a photograph of their reflective laptop display) screenshots of the shows and movies they’re watching.
For a history of Dumb Restrictions on Media (aka DRM):
https://en.wikipedia.org/wiki/Digital_rights_management
This fight goes way, way back. Microsoft worked with the media industry in the early 2000s to create a fully-encrypted media input/output pipeline for PCs in order to combat Linux adoption. Microsoft knew that it would be impossible for open source software to decrypt the media streams without making the encryption keys available so they went way out of their way to make sure things like HDCP would “protect” the media being played back on a PC from “illegal” copying.
It starts with the TPM module in your motherboard/processor and continues outward all the way though to your HDMI monitor (which has to have the hardware keys necessary to decrypt the content).
BTW: The keys for HDMI HDCP have long since been leaked so you can now cheaply and easily buy all sorts of HDMI capture devices on the cheap from places like AliExpress (they don’t ask any questions). Get one of those and your PC won’t even know that you’re capturing screenshots.