Cute little baby, Hazy, very nice.
I am not sure about ballast, but bulb definitelly lasts healthy longer if permanently on.
Factors of wear come mostly from on/off cycles versus the total on time. The highest wear occurs when the HID burner is ignited while still hot and before the metallic salts have recrystallized. https://en.wikipedia.org/wiki/High-intensity_discharge_lamp
I run my HS1 24/0 and it is true what Tang says. No visible difference in growth and light defficiencies on upper leaves. Not severe, but looks like Mg def. and does not get away with adding Calmag. But not getting worse so far. But I would be happy with invisible difference too and as long as plants stand still and turn leaves towards light source it is just fine. I position lights so that light is not top-down, but angled and I see that leaves are permanently sucking light and stay turned towards LEDs.
And I run them so, because they are effective, burn little fuel and are not very strong, only 75W used per plant. With stronger light per plant, lets say I would use 2 HS1 on a single one, I would not dare to run 24/0.
There are many factors to consider when deciding about 24/0 but I think we all agree that it does not bring big changes. Well, some of us hope for small ones at least.
Good Luck!