The thing is, a larger blade means a slower attack, a bigger wind-up, a longer recovery, and limitations on how many different ways you can actually swing the thing. You can bring up an attack with, say, a 60 cm sword from below easily enough, but you'd have to be really tall to manage that with an 80 cm sword, and it's basically impossible to do with a 100 cm sword, and nodachi are even longer than that. Similarly, if you're fighting in a narrow alley or hallway, like often happened when you invaded castles or keeps, there's just not enough room to swing a field sword. You'll just bang it on the walls.
It's not strictly about the dead zone the sword has, it's about another fighter being able to get close in while you recover and hit you before you've made your second strike. This isn't an issue on horseback, and it's not always an issue on foot in the field, but it's just not practical in all settings, hence the shortsword.
Also, you'll note that Japan wasn't the only nation that had the trend of smaller shortswords. In Renaissance Europe, there were a variety of settings where heavy armor and swords just wasn't practical, like onboard the cargo ships going to the new world, or against muskets. That said, the need for a sword was still around because it took for-freaking-ever to reload a musket, and their accuracy was pretty terrible (which is why warfare was the way it was in the 18th century, one musket ball probably won't hit anything, but a wall of flying lead can take out an entire line of soldiers). As such, a variety of light swords were made that enabled a wielder to make an attack without throwing off their balance, and what was eventually figured to be the best version of this weapon was the smallsword, since it was too fast to be blocked easily by the heavier rapier or colichemarde, and strong enough to knock away an attack from either (probably because of the quality of the steel being used in weapons at this time).