My .02$ worth.....Somebody correct me if I am wrong, but in tourneys "foigning" (ie:: thrust) was considered , if not a foul, at least bad form....This was most likely because of the danger it presented....As the romans said "two inches will kill a man"....In real battle you would use whatever means you could to kill your opponent....But in tournaments where capture and ransom was the money maker they tried to limit the fatalities.
As for the more rounded points....lets say you have knocked your opponent off his feet....A good hard downword thrust even with this kind of point should be effective....I stabbed a uncured ham covered in mail and while it did not penetrate the maile, it did sink in a few inches....a sternum shot or to the throaght would be incapacitating if not fatal.

Thanks for the leads, Greg. Part of the reason for "dismissing" I.33 is that some of the attacks that are illustrated are only designed for people out of armour, and when wearing maille, they are not as effective. Not so much as a civilian/military, but more un-armoured/armoured.

The comparatively broad, long types of the high middle ages would obviously suggest that the cut was the prefered mode of attack. However, this does in no way mean that you could not thrust with these swords.
In an environment where heavy armour was not standard issue, a thrust with a broad blade would actually cause more damage that narrow blade, in the same fashion that hunting spears and arrows where generally broad bladed.
Specialized thrusting blades only become necessary when dealing with heavy armour.

While mail does give protection against stabs, it does not provide sufficient protection from blunt trauma, spears and daggers to the armpits to warrant the development of specialized weapon to deal with it. (apparently)

Another major issue when it comes to the design of sword is shield use. In the high middle ages, large shields would be pretty much standard issue. And it is a lot easier to get around a shield with cuts than thrusts.

Once plate armour, especially greaves and poleyons, and helmets that cover the side of the head, becomes common the cuts are no longer effective. Which promts the development of specialized weapons for defeating armour.

Thank you for the extra documentation, Luka. Those are two books I keep meaning to get my hands on, when I get some spare cash, and find them "on sale".

Depends on the size and shape of the shield. I fight with a large flat-topped kite (in an SCA context) and when held across my body as semi-indicated by paintings and tapestries (covering chin down), I am nigh-invulnerable to most thrusts (including spears, unless 3 or more decide to gang up on me). I also tend to lose almost all of my lines of attacks except for overhanded thrusts/flat snaps (that part about the shield and sword occupying the same space at the same time adn the universe exploding thing). Seeing as how the imagery also has those guys on horses, I feel confident in suggesting they may have simply ridden down their opponents, while concentrating more on defense with the shield.