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OB1 can you provide a rules reference to back up your central assumption that there is such a thing as a 'Large Greatsword'? As my understanding of the rules goes - often demonstrated to be shaky! - there is no such thing; simply that many creatures of Large or greater size also happen to use more dice with their attacks, as a way of giving the image of big, hefty swings. I further understand that the system basically mandates 'damage per CR', and that creatures reach that level through lesser or greater number of attacks, and that big creatures (Giants, etc) tend to have fewer attacks for larger proportions of the mandated damage. In other words, there may be a CR 5 ExampleGiant that is Large sized and does 2d8 damage in one hit with a Longsword, and a CR 5 ExampleHumanoid that is Medium sized may do 2d8 damage in two separate hits, and we are not meant to assume that anything meaningful is being said about the weapon difference between the two.
For the same reason, just because a Bugbear does 2d8 damage with its club, does not mean that a human fighter - or even a PC Bugbear! - can pick up said club and do that extra damage; the game spells it out in that instance, to be fair, but I thought that the essential point is the same in all cases. Giants do 3d8 damage with their clubs not because of the clubs, but because
they are Giants, and their fighting style, size, muscles - whatever - means that they do that damage. If a PC grew to their size, and could wield said club, (s)he would not do that 3d8 because they are
not Giants and thus do not get to use their rules.