Anything more granular is marketing and advertising BS which they have no need for.
They could probably figure out watch preferences with good statistics, (and do), but asking for age probably gets them in the right ball park a lot faster.
Tying things from what you watch to what you might want to watch will be miles more effective than your age, because your age has nothing to do with what shows you watch.
I've known parents to show their kids "The Passion of Christ" or "Monty Python and the Holy Grail." I also know parents who watch (and love) shows like Phineas and Ferb or Spongebob.
What? I apologize, but that is absurd. Entire industries are built around the idea that people of different ages _generally_ have different tastes.
Take the "children's" television network Nickelodeon - someone realized that kids like different shows than adults, so they made an entire, 24/7 tv network dedicated to it.
Then they realized that kids go to bed at an earlier hour, so they made "Nick at Nite" for adults where they showed reruns of old tv shows. Then they realized that really young kids like different shows than older ones, so they made Nick Jr. Then they realized that ~college age people liked different shows, so they made Adult Swim. Then they realized that some older adults wanted to watch classic cartoons so they made Boomerang.
These weren't one-off "oh, one person likes different shows". These were entire age-based demographics. And this is but one example, plenty of industries - especially entertainment industries - target exactly this.
And plenty of hard science is based on the fact that human brains "mature" and adapt over time. Young kids brains are different that geriatric brains,
That is not to say any of this perfect. As these algorithms collect what a person does and doesn't like or watch, they can and should change.
And if someone wants to show their kids "age innappropriate" material to their kids, that's there choice. But don't recommend "The Human Centipede" to a three year old when they turn on the tv, and don't recommend Cocomelon to me.
I don't want to watch children's tv shows. They have never suggested children's shows to me.
My children don't want to watch bloody horror movies. They have never suggested bloody horror movies to them.
Sometimes I have to search for what I want. That's fine. Sometimes I don't, that's even nicer.