Why stop there? They should be able to dual wield Greatswords and a SHIELD.
About that, just check this one . This is Jan III Sobieskis ( Polish king from may21 1674 - june17 1696 ) sword, sheath and a hat which was blessed by a pope Innocent XI. You can still see it in a Wawel Castle ( museum ) in Krakow Poland. Whole length of this sword is 200,6 cm. Anyway in the same museum You can see a twohanded swords, longer then 2meters which was used by Polish knight in fights to cut off horse legs of the enemy cavalry. So my conclusion is that swords long like this existed and stil You can see them, but for sure You can't chop a tree with one hit )