I agree with you on that point: Video hosting is extremely expensive. This is why YouTube is basically a monopoly, despite most of its users being annoyed with it (I presume).

And isolated, without the rest of Google and Alphabet, it may not be profitable, despite all of the ads it feeds us. But from my understanding, YouTube is yet another data aggregator Google uses to make money. Indirectly I bet YouTube is very valuable for Google, even if YouTube itself is not profitable.