There's no particular merit to high voltage over high current, or vice versa. You can design an electric motor to run on higher voltage at lower current, or lower voltage at higher current, and both motors will work fine. Battery cells can also be connected in series/parallel arrangements with higher voltage and lower amp-hour capacity, or lower voltage and higher amp-hour capacity, giving the same energy storage capacity, and either of those will work fine. Neither configuration has any inherent advantage over the other. Neither is guaranteed to get you more range, or save weight, or package better, or have any other clear-cut advantage.
Each configuration does have small advantages and disadvantages. The high-voltage configuration, since it uses less current to deliver the same power, might weigh a bit less because the wiring doesn't have to be as heavy-duty. You might save a couple of pounds of copper by using smaller-gauge wiring. (But maybe not, since it might require heavier insulation to be safe at the higher voltage.)
Lower voltage is definitely safer. I imagine most of us Americans have been zapped by 115VAC line voltage, which isn't pleasant but it generally doesn't do any permanent damage. The Zero's 116VDC battery would do about the same if you inadvertently came into contact with it. But the 350VDC Tesla battery pack could do some serious damage, could even kill under the right (wrong) circumstances. My understanding is, that's why Zero designed for lower voltage and higher current -- it's demonstrably safer, to service personnel and rescue personnel in the event of an accident.
As far as fast-charging harming batteries, that used to be pretty universally true. But battery technology is moving forward very fast, and there are a lot more fine points to the story now. Li-ion batteries have a lot longer lives, and can tolerate much higher charge and discharge rates than they could even just a few years ago. This study:
http://www.greencarcongress.com/2014/09/study-finds-rapid-charging-and-draining-doesnt-damage-lithium-ion-electrode-as-much-as-thought-.htmlseems to show that the damage to Li-ion cells by fast charging isn't as great as we once thought, or maybe as it once was. Granted it's a four-year-old study, but the point is we just don't know everything about the newest generation of batteries yet. I seem to recall seeing a study with similar conclusions about fast-charging Teslas a while back, but I can't find it now.
BTW, this article:
https://insideevs.com/lets-look-at-tesla-model-s-x-battery-degradation/shows that Tesla, in the real world, is managing to provide some outstanding battery life, presumably with a mix of supercharging mixed in. These ain't your daddy's batteries.