What does it mean to culturally still have muster?
On the ground, 'Pagan' still has a meaning to people. It evokes idea of nature worship, multiple Gods and a rejection of Christianity. Shamanism and Wicca are two of the fastest growing religions in my country, so I think it's fair to say that at this point most people have been exposed to it since at least the 60s and possibly further back. So culturally it has muster, it means something.
And is this "too vague" attribute "meaningful at times" or simply convenient (if not necessary)?
It's necessarily vague as Paganism can be a vague concept. It's a good generalised term to broadly fit people who are not Abrahamic and who follow, generally, ancient and reconstructed religious paths. I think this thread can demonstrate that meaning holds some sway. Terms like 'Druid' and 'Kemetic' can be more nuanced. But some Pagans don't want nuance and prefer the eclectic and syncretistic nature of many paths, for which the vague, non-nuanced 'Pagan' works quite well if they want to repudiate specific paths because they follow many.
Confronted by extreme islamophobia in the wake of 9/11, one of the first things I did was go to the largest Islamic bookstore in the area and purchase a recommended Qur'an. So perhaps this will help: If I wanted to become a Pagan or pagan, what one book would you recommend as required (or at least extremely useful) reading?
It would depend on which Pagan paths you are interested in. If you wanted primary texts I'd advise various Egyptian 'Books of the Dead', or the Eddas, for example. I wouldn't really be recommending books though (I know this isn't the answer you're looking for), because most if not all of these paths were not book based and were and are based on praxis. In that vein if you asked seriously I'd be much more likely to recommend systems of divination, such as runestones or oracle cards, sticks or some other method. The cards are good because they explain a lot about individual aspects of the faith, Gods, trees, animals, rites, etc. I'd say I've learned more from the cards than from books. I'd recommend trying to communicate through prayer, creating an altar, making offerings and so on. I found that when I became a Pagan years ago, I tried books but found myself gravitating away from them in favour of ritual. As
@Quintessence has pointed out, what's in people's heads is not so much a bother, but what they do.
I'd be loath to recommend a single book on Paganism, as many are woefully inadequate, and I wouldn't lie to you by saying I believe any are up to the task. What I would do is recommend books about individual paths: there's a series of books that do just that, which I would advise
The Celtic Myths: A Guide to the Ancient Gods and Legends: Amazon.co.uk: Aldhouse-Green, Miranda: 0884282151809: Books (there are Norse, Egyptian, Japanese etc).