Well, what do you mean by "benefit"? There is no technological advantage, other than not needing a supply of electricity and the inability for whatever is written to be intercepted electronically (unless someone installs a keylogger on it, which has happened in the past, though of course not to me).
Personally, I like the immediacy of it. I type and there it is on the page. I don't need to print anything because the act of typing actualizes a product. I also like the feel of it. Pounding away on the keyboard makes a real product, so the work is more tangible. Then of course, there is also the fact that it is imperfect, which means that I have to think about what I'd like to write instead of barfing whatever trickles down my brain stem and into my fingers, or else waste ink and paper.
For someone who writes, different writing implements, like different pens and different typewriters, or even different computer keyboards (for example, an ergonomic keyboard rather than a laptop keyboard) is akin to a painter with different brushes, paint knives, palettes, canvases, paper, boards, etc. In my experience, the way that something is produced can have an effect on exactly what is produced. To use another analogy, musicians might think similarly in terms of music theory, but the instrument they play will influence the music they create. For example, on a saxophone it's really easy to create complex runs of notes and to play notes very quickly due to the setup of the valves and keys, unlike say, a slide trombone.
On a computer, I can take whole passages of text and easily chop them up and edit them on the fly until I hit on something. On a typewriter, I have to think about what I want ahead of time and generally proceed with more consideration as I work toward shaping things toward their final form. On a manual, this is slowed down even further and there is a lot of room for error, which can sometimes lead to interesting new ideas.