Why there is no merge point command in Adobe Illustrator?

I drew a circle, removed half of it, then drew line, connecting half-circle ends.

Now I need to make it united shape:

Searching Google and SE told me, that this is IMPOSSIBLE. Provided solutions are one is more incredible than another.

I can't imagine, WHY it is impossible? Why an application with such long history has such obvious lack in functionality as if it was written by schoolmates?

The question is general and the situation is general: suppose I have exact parts of desired outline shape. I can't use any averaging or pen tool, because all anchor points are already in place. All I need is just declare some overlapped points pairs as single points.

Why can't I do that?