Actually, the two handed sword was not all that unwieldy in combat. I have read some manuals, and seen a demonstration by the british museum, that showed how you could be pretty damned efficient with one of those things. First off, most of them have the ricasso (the area immediately in front of the crossguard) dulled, and flattened on the edges for a reason. The user could swing, and thrust the sword, and then grab the ricasso, and actually swing the pommel around, and use it as a club, or to hook an opponent with the crossguard.
Example: Braveheart - Despite it's myriad historical inaccuracies, you can actually see Mel Gibson use his Claymore to both correctly deflect a blow, and grab the ricasso, and use it as leverage to run someone through.
In the hands of the right person, the two handed sword could be as deadly as any other.
And most of the casualties of medieval battles were either caused by archers, or cavalry, or were actually due to POST battle infection. Their idea of curing a sword gash was to stitch it shut with just about whatever was available, and cover it with a rag. Add to this that hygiene wasn't very high on anyone's list, makes for one big pusball.