But you're right, of course. (Also, Aragorn might have died of tetanus, or an infected, minor wound; though there is an implication, in LOTR, that within the world of the story, the Elves have a brought to Middle Earth a sophisticated knowledge of medicine, along with everything else. Aragorn became a reknowned 'healer', etc, from staying with them. So you're right; LOTR inhabits a different world altogether from our Middle Ages).
We can't remotely imagine the shock and horror it must have been for men like Robert Graves and Tolkien, to know only picturesque townships and bucolic landscapes, and THEN abruptly be thrust into the hellscape of the Western front. (The recent movie, All Quiet on the Western Front is extraordinarily good at showing how hellish it was. Brilliant, in that respect, though I warn you: it is not a good time). But again, these considerations, regarding history and the culture of the past, are utterly beyond the scope and capacities of the neo-feudalists. They have no conception of the world they're creating, nor how ill-suited they are to inhabiting it.