Yes, populus and vulgus are basically synonims, with vulgus having the worst connotations ("folk" VS "the mob" basically), but semantic sliding and usage have made "popular" and its derivates get a base connotation. People don't as easily link "divulgation" and "vulgar".

It'd be nice to have a word that basically means "spreading elevated knowledge to the untrained" without making it sound like we're abasing it. Every time I hear the term "Popular Science" I think of Dr. Sheldon Cooper deriding and ridiculing any of his colleagues who are trying to do just that.

Pleased to meet you, Dr Gablehouser. How fortunate for you that the University has chosen to hire you, despite the fact that you’ve done no original research in 25 years, and instead have written a series of popular books that reduce the great concepts of science to a series of anecdotes, each one dumbed down to accommodate the duration of an average bowel movement.

That sort of elitism just makes me sick*, and I've seen it in Real Life, even among scientists and from scientists towards engineers ("The Oompa Loompas of Science", another Sheldonism)..

If only for self-serving reasons, it is very counterproductive. The more people know about Science, the more likely they are to understand the importance of any given work... and fund it. Also, the more likely they are to show respect to science-folk and freaking listen to them. That means investing time and effort to make this stuff reach the masses, and it's perfectly understandable that a researcher spend their entire career on that: understanding scientific concepts proprely and then managing to grab untrained people's interest and eloquently explain advanced concepts to them so that they grasp even a pale reflection of them is not trivial.