Cap'n Kobold
Hero
Bear in mind that the zweihander is on the top end of a scale that starts with the historical longsword in the '5e greatsword' category. Historical longsword is a little shorter, quite a bit lighter, and (depending upon style/purpose) is used for thrusting as much as slashing. Against a single D&D longsword its a very unfair matchup. (Of course D&DE longsword-type swords were almost always used with a shield, which changes things drastically once again.I completely agree. In D&D, if you are going to fight with a 2 handed weapon, a 2-handed sword (historically a claymore or a zweihander) is much better than a longsword (finally, in 5e the long sword is equivalent to the historical weapon). HOWEVER in real life a long sword is a better weapon 90% of the time - you may not be able to cleave someone in half but it's much, much faster and better defensively too. This bothers me.
You can get a bit of extra power with two hands, but you're right in that the design of the hilt isn't designed to incorporate this: one hand would be covering the other.There I disagree on many of those (esp arming sword, falchion, viking sword). The sword handle was short (esp a viking sword) and there is no room for a second hand, baring half-swording (a maneuver that wasn't done on either viking sword or falchion anyway). If I was to stat such a weapon (and I did in my game, the tulwar) I would give them 1d8 damage, strength, slashing, non versatile.
I just don't really regard the (admittedly considerable) difference provided by a longer hilt to be worth creating a new category of weapon that would be the same as the longsword entry but without versatile. (OK. maybe also a bit lighter and cheaper, but these aren't major differences IMO).
A character that uses longsword and shield with a Viking theme for example, is probably going to be using two hands on their sword so rarely, the difference just isn't going to come up as significant.