Why is quick share buried in the settings menu, instead of being an app?

Especially when receiving a file, it makes no sense to start by going into settings.

Generally, you don't have to open settings. The the built-in share menu from a file has quick share as an option and if someone shares something with you, you'd get a notification.

You can add it to the quick settings tiles in the notification shade, they show that exact flow in the blog post.