Damage up is actually not that great, you can read about why
here. It really only helps charger users since it allows them to kill on a lower % of full charge. With other weapons it doesn't reduce the number of hits needed to kill so it does almost nothing.
There is one often-overlooked way in which Damage Up can reduce the number of hits required to splat--namely, when you're using Burst Bombs in combination with your main weapon. For instance, in the case of the standard Splattershot, Damage Up can allow you to kill with a direct Burst Bomb hit and a single shot, whereas normally you would need to follow up the bomb with two shots. And if you take Burst Bomb grazes into consideration, there are even more thresholds you can aim for. (For instance, if you use the Slosher, Damage Up can make it so even the minimum graze damage from the Burst Bomb is enough for you to finish the job with a single slosh.) Really, due to the way Burst Bomb damage works, pretty much anything that uses them can benefit from Damage Up, but weapons like the Splattershot benefit even more.
It's also worth noting that since rollers are not affected by a damage cap (not even the individual pellets they fling), they actually can benefit from Damage Up. In this case, instead of reducing the number of hits needed to splat, it would instead increase the range at which the roller's ink fling could kill.
Lastly, as mentioned by Pyritie, there are a couple weapons that are particularly vulnerable to Defense Up, so a certain amount of Damage Up to counteract users of Defense Up is a wise investment for them. (This is particularly true in the case of the .52 Gal, since the two-shot splat is the main selling point of the weapon and it only takes one Defense Up main ability to nerf it down to a three-shot splat.)