

It depends on how nerdy you want to get.
Generally no, That checkmark is cloudflares multi-million dollar product that protects half of the internet from bot abuse. If there were a quick and easy work around then the bots would quickly learn and adopt it too. Sadly, it has a real penchant for triggering for regular users when you’re using hardened browsers and VPNs as well. It would be nice if network admins cared a little more about sticking it to the man and using bot protection alternatives instead of just proxying through a cloudflare tunnel and calling it a day.
If you’re slightly tech savvy and lucky then the site allows web crawlers/indexers or has RSS feeds. This lets you use an RSS feeder or a text scraper like NewsWaffle
What youre describing with saving a cookie to prove your identity is actually do-able, yt-dlp uses this to download age restricted content but getting that cookie extracted into a text file is a non-trivial nerdy thing the average person cant be trusted to do.
Your welcome! Its good to have a local DRM free backup of your favorite channels especially the ones you come back to for sleep aid or comfort when stressed. I would download them sooner than later while yt-dlp still works (googles been ramping up its war on adblockers and 3rd party frontends). BTW yt-dlp also works with bandcamp and soundcloud to extract audio :)