-sigh-
I.33 - ????
Wittenweiler - 1500
Tallhoffer - 1459
Dorbringer - 1389
Oakeshott's typology
All armored combat treatises from varying fencing schools, none of which referencing absurdities as partially sharpened swords, or swords only sharpened at the tip. Some true and false edge, maybe a little ricasso here and there, but no bullshido. I wish I could give you some British or French texts, but unfortunately they were busy duking out over a parcel of land. However,
British-museum.org
ARMA's official website.
Alexandria arms collection
Alexandria arms again
All clearly having very sharp (or remnants thereof) of perfectly sharp blade. I am well aware of Italian dueling swords and am also well aware they they were a fad. It appears to me you're basing your entire perception of swords in the medieval world solely on the musings of an Italian fencing teacher (creative anachronism indeed). Considering you couldn't even be bothered to get halbschwert right, it wouldn't surprise me in the least. You can totes halbschwert a razor sharp blade and it was frequently done.
I don't know what I expected, arguing with a glorified LARPer.