Then it's not piracy.

technically it can, but not for free. if you have a subscription to access the media, the site is supported and drm-free, and you have a way to pass the account credentials to yt-dlp, it will download. if it plays inside a browser with drm disabled, yt-dlp can likely get it for you. you could download stuff from crunchyroll that way before they added drm. if it does have drm, you can still download the encrypted stream and decrypt it later with something like gpac if you have the keys, but that's a bit besides the point.

however there's very little supported sites now that have paid subscriptions and no drm. and in neither case is yt-dlp circumventing anything, it cannot access something you had no access to in the first place.

AFAIK, most streaming services have some sort of a DRM system that won't let you screen capture a video. Not like it is impossible to circumvent. Not even hard, I may say. But it is still there.