Close! DE. Still mid-atlantic coast, anyway. My friends actually call brush axes “clampoons” because one of them used to always loudly sing “The Ballad of Reuben Clamso” whenever he was using one. But brush hook and brush axe are regional usage.
It looks very unlike a near eastern scimitar to me; I’d categorize it as a double-edged sickle sword. But I’ll check my copy of Stone since that’s what Wikipedia’s article cites.
You could use a shotel like a pick for over-the-shield strikes, but it wouldn’t be as effective due to being lighter. Picks punch through helmets. It’d be a great hook for opening up shields for spearmen in the second rank, though.
EDIT. Stone says “The Abyssinians have no idea of fencing and use this extremely awkward weapon to strike over, or around, the shield of an opponent.” It sounds like it was used more like a one-handed pick than a sickle or scimitar.
In practice, the khopesh and the scimitars/matchetes with exaggerated tips do work much like light axes - the tip-heavy balance gives leverage to deliver a more powerful blow out near the tip of the sword (I’m going to avoid saying things like foible or terzo).
But axes have small cutting edges compared to tip-heavy sword forms, which not only provides less attack surface, it also makes an axe easier to block or parry and more likely to get stuck in things.
In art you will mostly see the more extreme forms of khopesh & scimitar because they look cool. You’ll also see very tip heavy blades used in sword dancing because the closer the balance point of the sword is to the center of the weapon, the better looks it balanced on your head or hip. It’s aesthetic. But less extreme forms were common; the heavier the tip, the more powerful the chop, and the more difficult it is to execute the thrust. Your fighting style and your opponent’s armor determines what works best.
In my opinion, the best all-around one-handed sword design is the stereotypical viking sword, and the best all-around two-handed swords are Japanese daito (most of which are actually bastard or hand-and-a-half swords). Neither form is tip-heavy. But really “best all-around” is not a very useful metric, since each sword type has strengths and weaknesses that can be exploited in both attack and defense. I would rather have an estoc than a katana if I was part of a cavalry charge against armored foes, for example.
