RAW is RAW. It doesn't have to make sense. By RAW it doesn't matter how long actually is a weapon. What matters is what size is it's intended wielder and what special abilities it has.
In this case the RAW is kind of bad but the way I see it, Dannyalcatraz is correct in emphasizing the wording "of the appropriate size". RAI this would indeed translate easily to "double the standard reach of this size category".
Let's say I give a choker a small spear. He has a base reach of 10ft. which is not standard for small size. It's because of his special abilities. Clearly I would rule (as a DM) that his spear only adds 5ft. to his reach since it's not scalable to adjust to the arm length of its current wielder.
The problem I see with your argument is that you determine special abilities to be on par with size category in this matter. There has been no mention of that anywhere. Actually, the "a wielder of the appropriate size" part states that only size matters RAW.
I'd think of it like sneak attacks / elemental weapon enchantments and critical hits. You don't double the extra damage added by a special quality. Rather, you double the standard and add special qualities on top.
P.S. I don't know whether the OP enjoys munchkin cheese or not (probably not since he's going with a knight) but maybe we should consider the in-game effects of a character having arms which are longer than he is tall, no? Also, his DM might just rule something mean about the use of armor with the arms in question.
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