This is why the Mordhau was a common technique in medieval armored combat. The knight would grab the blade of his sword and bash his opponent with the pommel.
I have to say that if you're a knight, and you're developing techniques like holding your sword by the blade to bash a guy with the handle because you know it will be more effective enough to bother, you're way too fucking stubborn. Any knight who wasn't a blockhead would be using a mace. That's what they're for.
If this was actually a common thing, my appreciation of warriors of old has dropped immensely.
But that would require having a mace with you, which might not always be possible or practical. (When you're running around with 30 kilos of steel on you, and your ability to stay alive and do something useful depends on you not getting tired out, you probably don't want to carry more weight than you have to).
From what I've seen of medieval sword-fighting manuals, and demonstrations, it seems to be more about "how to win a fight when you have a sword, and your opponent has one too", rather than modern notions of swordplay. And an important part of that is knowing that the handle end of the sword contains lots of hard, heavy projections that can be used to bash (or hook) people with.
(Indeed, this was part of the design; the and crossguard and pommel, as well as having the obvious purpose of protecton and balance, were also intended for hitting people with. And the ricasso (the part of the blade closest to the handle) was often unsharpened, so you could hold it, either for the purpose of bashing, or for half-swording (what the other guy in the picture is doing:
http://en.wikipedia.org/wiki/Half-sword).
I wasn't around at the time, but I suspect the good sir knights preferred slaughtering unarmoured peasant levies from horseback and only engaged other armoured knights in melee when no other option was available. A longsword is then a good choice. A quality sword was mandatory bling for a proper knight in any case, a mace is so uncivilized.
Actually, maces were also seen as symbols of authority, and perfectly appropriate for a knight. Originally, I think, because as a blunt weapon, they were useful for pushing people around with, or giving unruly servants or reluctand soldiers a slap, as well as for pointing