If the Grim Reaper can kill you with one touch, what the hell does he need the scythe for?
For greater reach, with the additional benefit of being able to bring the soul closer to himself afterward. Plus he doesn't get his hands dirty. It's also more useful for groups.
To be a "reaper", and thus carry out a convenient metaphor. Without it he's just a skeleton in a dress.
Potential modeling career aside, one of the things about this guy is how depictions of him vary. Sometimes a robed man, sometimes a robed skeleton, and sometimes no robe at all. (Ever see that image of a European floating stage with a giant skeleton reading a book?) Information about him is spurious and probably conjecture; in the best case scenario, he is most often seen by dead men, and you know what they say about their tales.
No one ever said he needed it.
What's more efficient: plucking one blade of grass at a time, or, aha, scything through an entire field?
So extending the "Reaper of Souls" analogy, that implies that there must be an eater of souls. Probably a miller and baker of souls too. Delicious soul beer perhaps. Why else use a grain analogy otherwise? Well I suppose you could mow the lawn with a scythe, but that implies a compost of souls. With this sort of fate in store, is there any wonder people fear the Reaper?