Bear in mind that most quality fonts aren't actually freely available, typography licensing is a complicated maze and for large for-profit companies often wildly expensive. Creating a custom typeface is expensive, sure, but it helps in establishing an identity and it also alleviates huge licensing fees.
Its similar to film scores to film/tv. Its not immediately noticeable to most people unless you take it away.
for example if you play the benny hill theme during lord of the rings fight scenes, it completely changes the feel of the scene. Whilst not as powerful, if you change the font for bbc/nyt/$other news org to comic sans, it has an equally powerful effect.
So just use an obscure free font?
For a lot of large companies, "free" fonts aren't free. They need to be licensed. If you're going to do that, you might as well just make your own. The upfront cost _might_ be comparable, but the ongoing costs are almost zero. Also you don't need to re-license if you make an new app or something similar. For about $50k you can have a font of your choice, which is free to use as you wish. Moreover you can create derivatives without getting into trouble.
I'm not sure how much it costs to license a font for something like a newspaper/online site. But its not insignificant.
Its also another way you can wield a ban hammer if someone is ripping off your work.