We don't need to have an attitude about it.
Healing does not generate damage. That's not to say that it's useless because that's obviously false, but the point of saying whether something DPS negative, neutral, or positive is to signify where it stands in relation to your neutral game, and that applies to every job. Why cast Phlegma when you could cast Dosis instead? Because Phlegma is DPS positive: It deals more damage than Glare. Why minimize uses of Prognosis in favor of Dosis? Because Prognosis is DPS negative: It costs you a cast of Dosis and should be reserved to situations where other resources are unavailable, or you don't have time to heal through multiple weaves and need to layer an OGCD with Prognosis to heal faster. Why not cast Pneuma on cooldown rather than wait for a situation that best utilizes the healing? Because Pneuma is DPS neutral: you neither gain damage nor lose damage when casting it, thus there is no need to use it as often as possible.
I get that you're saying Pneuma offers more than Dosis because it also heals, but the point I'm trying to make is that extra healing doesn't matter when calculating damage, which is primary the purpose of the negative/neutral/positive language. That's why we don't typically count Pneuma as a true DPS action, because we choose to cast it for when the healing is needed, not the damage. If the damage were higher than Dosis, that would make it a true DPS action, because then you're incentivized to use it on cooldown, but that would also conflict with the healing effect since you won't always need it every 2 minutes on the dot. But that's also why I'd suggest changing how it works in some way to allow Pneuma to serve both the functions of damage and the function of healing when appropriate. For example, make Pneuma a raw damage burst on a cooldown, but make Eukrasian Pneuma a DPS neutral heal with no cooldown but a steeper MP cost. That not only retains the current function, but gives you more agency over how often you want to utilize the burst healing effect. You can be greedy with it, or you can be frugal with it. Letting you choose is something the game could stand to do a lot more of.