My two pennies on this topic.
1. Accidents happen and people die in the most random of events. This is just one of Murphy's laws. It's not inconceivable that a trooper practicing drills with sword drawn, falls from his horse and hits his head against his sword hilt. With the flat disk guard of the 1796 HC, a blow from the edge would have been nasty!
2. Officer swords at the time were private purchase and it would have been a personal choice to modify the blade (or order one with a spear point).
3. Officers had multiple uniforms at the time; undress for military exercises and battle, dress for parade and functions and full dress for when on formal functions. Often this ment a different sword for each uniform. While the evidence is thin, it is broadly accepted that the dress sword for officers of the heavy cavalry was a double edged spadroon with a boatshell guard. with some cutting capacity, this sword was best suited to thrust based attacks.
4. The removal of the langets; my understanding was that were rather fragile and had a habbit of breaking off, so it is possible the other was removed to balance it out. I have seen examples of swords with a single langet remaining.
On a side note, the 1821 regulations for the British lancers specifically mention three different swords for undress, dress and full dress. The last two being mameluke sabres with a steel scabbard and a valvet covered scabbard respectively.
Because posts are best with pictures:
1796 Pattern HC troopers sword:
1796 Pattern HC officers undress:
1796 Pattern HC Officers dress:

The leather scabbard could mean that this was for full dress, or that it was worn by a general officer who were also known to use this hilt.
And to show that Georgians liked to be difficult and throw the odd spanner into our nice modern categories:
1796 Pattern HC Officers dress with family broadsword blade: