I don’t think Joy is interpreting your question the same way I was. From her interpretation’s perspective, I’m sure she is 100% correct.
My interpretation is you want a category term’s parent automatically assigned to the post as it is being saved. This is possible, but it’s kind of messy and requires custom coding. When a post is saved, the selected category term IDs are sent to the server. There’s no way to tell from this data alone if any particular ID has a parent or what it might be. So the code would need to get all the categories in existence and look up each selected ID to see if there is a parent and determine who that parent would be. And if you need the top level ancestor instead of the immediate parent (in the case of several hierarchy levels), it’s even more complicated. After all of that, it could turn out the parent was selected all along.
As Joy points out, an archive list of the parent category will include the children whether the parent was assigned to the post or not. Maybe you have other reasons for requiring the parent be assigned, but appearance in parent archive lists would not be a good reason.