Thanks for this very detailed discussion! I have two complementary points that come to my mind. First, the energy provided by the horse might actually require heavier, stronger swords so that they can reliably withstand the force of the blows dealt with the horse's strength behind it, be it cuts or thrusts - a slender thrusting blade would be at a much higher risk of snapping in the opponent's body on horseback than on foot. Second, regarding the length of the blade allowing for a more commited attack and being a way to mitigate a "less subtle" management of measure than on foot, I'd go even further by saying that for a moderately trained cavalryman (say the average 19th c trooper, not the knight), who cannot manage measure so well and cannot perfom complex, nimble techniques, the French recommendation of "just thrust and forget about the rest" works much better with a very long and very heavy sword such as a cuirassier's, because blade presence means authority in the bind. So even if the angle, the distance are slightly off, the chances of dominating the bind and the staying stafe while driving the thrust home are higher. In that "low technical level" scenario, nimbleness is actually irrelevant, since you attack your opponent only once with only one attack.

I remember reading that the Armenian Savaran could allegedly split a helmet with a single sword blow. Even if this is not literally true, maybe larger swords were designed in part to work more effectively against helmets (which cavalrymen would most commonly encounter of the footmen)?

My husband says "Yes because you are running on horseback and you want that blade to hit the opponent full force during battle...to cut through armor and/or all the outer protection they are wearing."

Off topic, but I want that chair...

I cover almost all of this in my journal article. I think this is one of the advantages of the longsword in the 15th century, as the weapon can be made 'longer' or 'shorter' by switching between 1 and 2 hands. Thus for mounted use it could be longer and more blade heavy, or on foot it could be used in 2 to make it quicker, or halfsworded for wrestling. www.tandfonline.com/doi/abs/10.1080/17416124.2019.1573963?journalCode=yaaa20