I'm not a zero sugar person, but close - I'll eat fruit, or some foods with minimal sugar added (peanut butter).
It's been way better for my health than my former daily ice cream diet. I've no doubt many can walk the tightrope, but it's much better for me to leave behind the sweets entirely. Stick with it long enough and it's not so hard to maintain, and it keeps maintaining weight much easier.
I can see it the same way on how drug abusers will quit it entirely and rather than trying to have a moderate take on using since it's too much work to be moderate. Although, sugar is not the same as a drug, the response of cutting the substance out entirely has some parallels to drug recovery. So the movement makes conceptual sense to me at least, and it's not like cutting it out is actively unhealthy. So I don't think it's a big deal to be a "zero sugar" person