Probably because Google is actively and frequently banning many Piped or Invidious hosts, and is generally currently at war with “alternative frontends” to YouTube in an effort to make users browse YouTube directly and consume ads there, or buy YouTube Premium. This is in line with their current fight for more ad revenues across their products and services. You probably have to either search for another public instance which isn’t banned (yet) from accessing YouTube, or host your own instance.

Yes, it’s a dangerous combination of media/IT illiteracy/incompetence within the general public and profit-driven proprietary social media algorithms that only aim to keep people engaged for the longest time, no matter the content they are being served. And usually, the more extreme the content is, the higher the engagement, the more revenue to be made from serving ads to the users and selling their collected data. This currently leads to a rise of misinformation, anti-scientific thinking, and so on. Which just so happens to align with extreme right-wing ideologies.

AFAIK, browser choice is still limited (as usual with Apple) because every browser on iOS needs to use Apple’s WebKit engine. That means they only differ in UI.

That doesn’t surprise me, and yes it was always because of anti-competitive practices, so I’m all for more neutrality, I’ll just add 2 shower thoughts:

1. Seeing that Brave is at the top of the browser list, I wonder how many selected Brave just because it’s at the top of the list and thought that this must be a good choice then, not because they actually like Brave.
2. It’s nice to have such a thing for browsers, but it would have to be expanded to other apps as well, e.g. mail client. Oh well, maybe in another 10 years or so.