Of course not, as long as you follow rules you will be safe, yes there are cases with false copyright claims but these are rare, for example, I have not encountered such things so far and there's no need to fear about Youtube rules. Do you want to start a YouTube channel? Do it right now, start working, stop wasting time. I was preparing todays video while I got this notification you quoted me if Youtube was that bad I would have stopped myself.
I respect creators that put time into uploading videos of high quality to their channels because I think YouTube as a concept is great. However, YouTube is owned one of the biggest corporation in the world, Google, and they want to make money. Sometimes this causes them to put their own interests before the content creators. An example of this is with the monetization.
Namely, YouTube's advertisers don't want their ads showing up on videos that'd potentially hurt their brand, causing YouTube to demonetize videos/channels that may fall within this category (this is also the reason to why you're required to have 4,000 watch hours and 1,000 subscribers before you can
apply for a partnership). Or at least that's how it's supposed to work. When demonizing happens to random videos/channels that haven't done anything wrong, YouTube always seems to not have anything to do with it. At least not until it has blown up on some other social media platform like Twitter or Reddit.
Just the possibility of abusing the copyright system is another example of this. If someone claims he owns your video, you're on your own. YouTube doesn't want to risk being sued for copyright infringement and will tell you that you have to solve the matter with the one that made the claim. Easy to say when your livelihood or even your channel (that you have spent hundreds of hours into) is at stake.
I'm glad you have never experienced any of this but let's say you wake up tomorrow and find out that your channel has been terminated. What are you going to do about it? Even though you'd have hundreds of thousands of subscribers, YouTube won't care. You're just one creator in the crowd.
Saying "copyright claims are rare", is just being naive. Sure, it may not happen to the majority of the creators, but just the fact that it's well-known among creators shows something is wrong. This has happened to close friends of mine, so small creators are as exposed as the big ones.
Just to add, there are a lot of other bugs, like when subscribers/views magically disappear, first reported many years ago that still hasn't been fixed. As a developer my self I find these bugs crucial, as it affects a lot of creators.
EDIT: This post may seem biased, but as I said, in the beginning, I think YouTube is great in its own way, and I find it hard to think of an internet without it. But as the matter with most big corporations, they don't look at their users as individuals, each with their own need; they "generalize" them.
Since they also the seek to make money, they often seem to put their paying users (advertiser/corporations) in front of their content creators, who, when you think about, actually are the ones that make YouTube to what it is.
Lastly, the advantages of a blog/website are that you don't rely on a 3rd part service, you'll get all the revenue for yourself (YouTube takes 45 percent of your ad revenue), and you'll start earning directly (YouTube require you to have at least 4,000 watch hours and 1,000 subscribers before you're able to place ads on your video, and they also have a threshold of $100 in order to withdraw your funds). Plus, no one will tell what you can or cannot do!