Yes, this is true. But many of the spells in question are divine. I can very easily see religions deciding that only things with truly divine origins can be used because anything else is impure.Respectfully, I genuinely don't think it is even remotely possible that a society would not develop those skills at all. Many modern Americans know how to manually start a fire and purify water, even though they've never had to use that knowledge in order to have warmth and clean water.
But anyway. My original point wasn't that nobody would do these things for themselves, but that, if people relied on a few individuals to cast spells to purify food (not just water), cure strange diseases, create fire without fuel, and other things that can't be done easily or at all with the technology at hand, then civilizations would end up centered on those people; they would likely have a high-ranking position.
The spell says "For the duration, you can sense the presence and location of poisons, poisonous creatures, and diseases within 30 feet of you. You also identify the kind of poison, poisonous creature, or disease in each case."And the spell would tell you that. The person identifying disease knows what the disease is. Knowing the name of it isn't at all useful, nor does it make sense when you consider the origin of the spell. It has to have had a starting point, and that starting point really can't be names of illnesses. Nor does the spell say anything about language, or common nomenclature.
Also note that you learn what poisonous creature the poison is from, if any.
I just don't really see any way for the spell to function without giving the caster useful information about the type of disease.
Also, just being able to detect disease in a radius around you would reduce the spread of disease, as you could much more accurately quarantine the sick than we can today. And since it says you learn the kind of disease, you'd know if it's contagious or not, at the very least.
It does not say that you learn the exact cause of the disease, meaning things like bacterial infection or mutated cell. You can decide it means that, sure, but I'm pretty sure it just means that you learn the people have koboldpox or were poisoned using giant spider venom or something similar; it might even detect lycanthropy, depending on if the DM decides that it's more like a disease than a curse. But I don't think it's going to go much deeper than that. Compare to detect magic, which says that you can spend an action to look more deeply at the magic to determine the school; or detect thoughts, which requires you to use an action to probe into the mind of the person whose thoughts you're detecting. Detect poison and disease merely says you detect the presence of such things and can identify what kind it is. But that's all it says. Anything else should require a Medicine roll, at least.
But yes, it will very much help to constrain diseases by making it easy to quarantine the infected.