YouTube made 17.9 billion profits in 2021 so they are definitely profitable. As it turns out having a search and video monopoly both makes you a lot of money and enables you to have massive control over the market. Google has already been sued many times for prioritizing it's services over others in it's search engine and it routinely introduces new search plugins that replace the services offered by other websites. the built-in weather app and travel info plugins are good examples. Even if YouTube wasn't directly profitable, the value of the data they use to further their own goals is more than worth it for google.
The argument that they are paying out any significant amount in IP infringement claims in nonsense. Section 230 of the communications decency act provides broad immunity to platforms that make a good faith effort in removing user uploaded content once they are aware it's infringing. If you look at a history of youtube copyright claims (
https://en.wikipedia.org/wiki/YouTube_copyright_issues), you can clearly see for the vast majority of lawsuites YouTube itself isn't the entity being sued but individual creators on the platform. YouTube has been extremely accommodating to IP holders to avoid any potential lawsuits, because even if they are likely to win they want to avoid lawyer fees.
Which is precicely why it's such a problem to have a company that has a monopoly over three of the biggest services provided over the internet (seach, ads, video) to command such leverage over the market. They are not there to provide value to customers, they are there to further Google's profits and hinder competitors. Given that the government provides the legal frame-work for google to exist in the first place and that they protect google IP, either Google should be broken up for the good of the market or forced to agree to binding terms and independent monitors. A lot of capitalists seem to forget that society is the one that provides the means for companies to exist and that wanton capitalism isn't justified simply because it's a for profit company. Markets should be open and free and companies preventing that should be punished. Striving towards a free market includes preventing any single market player from controlling the market. It's inarguable that if government control results in more competition or better outcomes for a given market, that is freer that a monopoly running rampant.
If they do not provide value to customers, customers either ignore their business or take it elsewhere. Value is relative and not always monetary in nature, as with entertainment it's often gauged by "enjoyment" that the individual takes from using the service. Google is big, but I do not hold it against them for being big. They've gotten there because people like their services, and have always found them to be reliable. That in turn generates them a healthy business. People don't say "I'm going to search for something online", they say "I'm googling it", because Google is the gold standard of search engines. Just as YouTube have become the gold standard of online video self-publishing.
For many years, YouTube had competitors such as Dailymotion, vimeo, Vine, Coub or BitChute (the latter of which became extremely controversial due to their refusal to kick politically incorrect content off their platform), none of these ever really captured much market share or became niche websites, and only now it faces serious competition from TikTok - to which YouTube responded by introducing their Shorts feature. It's a service who prevailed over all others of their kind, just like Facebook (orkut and myspace), Instagram (flickr), WhatsApp (Telegram, Line and Signal), Reddit (the entire fediverse), X/Twitter (tumblr, digg, etc.), Discord (Xfire), Twitch (livestream classic, or that one service from Microsoft that I don't even remember the name anymore lol, I think it was Mixer? flopped hard) etc. - some of them may not even be the most successful or the apps with the richest feature sets, but they are the services - and i mean services, not brands, you'll notice that X proves this once and for all - that stay with the people over time, and many of them have entirely supplanted and driven their competitors either into relative irrelevance or out of the market (refer to the alternatives I have mentioned in the parentheses), or in X's case, may not even have the highest number of active users but definitely the highest reach of them all.
As for the whole morality of data management and gathering and whatnot, it's not the subject, but no doubt that while most of us would like to retain greater control over our own digital identity, the only way to truly disappear from the online world is to unplug your computer from the Internet and be completely off-grid. You especially do not use any of Google's services if you have a genuine concern with being profiled and tracked online.
I am a capitalist. I believe in free market capitalism. I also acknowledge that if you aren't paying for something, you are the product somehow or some way. But I do not think we've quite reached the point where we can tell corporations that they should be obliged to practice different prices to different people just because they have a misfortune or another. That is definitely not "free".