Depends on who gets to decide what "false/misleading" is. I'm not sure how this could be any less transparent. I personally see less than no reason to trust YouTube's judgment in these matters.
Even bazaars like 4chan are moderated.
Now, in order to speak, you nearly have to go through one of Their gateways. If you piss off FAMGA (Facebook, Apple, Microsoft, Google, Amazon), you're gone off the net. Some of those gatekeepers are big scripts with no human intervention for your level. If you fall between the cracks, then you have no recourse, other than find a place like HN and beg publicly - lest you get shitcanned by the HN gatekeepers.
No, you're not. Not even close. The Daily Stormer is still online; you will be too.
Is the promotion of cats a political agenda? Can allcats.com take down videos of dogs?
Sure. Why shouldn't a private entity be able to determine what kind of speech they allow on their own property?
Youtube is a private service, thus they can remove content as they wish. Of course, most forms of historical media have also removed or suppressed controversial content. But in the old days it was preemptive. There was only so much room in a newspaper, you had to own presses and a distribution network, and they didn't hire just any schmoe to write columns.
It was a proactive system of censorship. They got people invested in a career of finding the proper stories and promoting what was acceptable to the establishment. Obviously common people could say whatever they like in their daily lives, but their freedom to put content into a newspaper or television show for all to see was extremely limited.
We have enormous freedom in self-publishing mass media today. So much content is being created that no mortal person can serve as gatekeeper and pick and choose what gets published like a newspaper editor could. So on one hand, we're living in a utopia of free speech. But new ways are being devised to automatically manage content all the time. And even though human moderators don't catch everything, but they slowly do what they can.
There are some genuinely harmful ideas out there, of course. Some things that ought to be restricted. Who gets to decide? Is it right for a private company to choose? I doubt it, but private companies have always been choosing what gets into media. In the past their decisions were much more totalitarian than today.