Why cut the whole hand?

[The Squatter of Amon Rûdh]

Aside from the other considerations, I think that Tolkien's sense of style played a part here. It's more mythic, heroic and impressive (ie simpler) just to cut off the entire hand with one sword-stroke than to take an arrowhead and start slicing pieces from the hand; besides causing poor Maedhros a great deal more pain, as Mister Underhill has pointed out.