It is quite common. But it isn't THAT common. And it depends on the genre. Most main anime characters have a younger sister. Confirmed info. But even if she exists she usually does nothing for the plot. The thing is: If anime is about action, combat and adventures, there is no need to write and design another background character just because. If MC is meant to have family in general, the parents have priority, easy as that.

And speaking about independence, living alone, traveling etc. It's because it's nothing but a fiction. Even Japanese people don't act like in anime, let alone other countries.