Is your entire system 120V single phase? Or do you use it to back up a house with 120/240V split-phase from the grid?
Feeding 120V only to one leg of 120/240V can cause brownout and damage to some equipment. If you feed 120V to L1 and there are any 240V loads between L1 and L2, then 240V loads in series with L2 loads get 120V total, each load sees less than 120V which is brownout condition.
We can lose neutral in a grid-fed circuit as well. I did that as a kid, doing "hot work" connecting power to my workbench, I opened neutral which burned out a light bulb in the house.
In a commercial site with 120/208Y 3-phase feeding cubicles, lost neutral put 208V across a power strip, causing it to smolder due to surge arrestor. We were told not to plug heavy loads into the cubicle wiring. The organization had an office copier (10A or so) plugged in.