My suspicion is that this practice is one of those things that used to matter but is now antiquated because of how easy it is to look things like this up, or that it's used to distinguish between X publisher in one place and X publisher of no relation in another place. Do any academics know why this is emphasized in so many style guides?
Specificity. Typing a few more characters makes it just that much easier for a reader to track down your exact source. It may be true at the time of your writing that there is no potential for ambiguity. That may not be the case in perpetuity.
To add to what /u/targustargus pointed out, many presses (think Oxford University Press, for example) had or have many regional sub-units. These did not, until very recently, have crossover catalogues; if you wanted a book from OUP Delhi, it was not necessarily available from OUP Oxford or OUP New York. Before the era of Worldcat that distinction was rather important. It is far less the case now, but many presses do still have regional branches or other entities under their umbrella with differing catalogues. So you're right that it's often unnecessary now, but that is not universally true, and may not be (as pointed out) true in the future.
In my own work, the place of publication has been important in two ways:
Raising historical questions. For example: Why did the Prime Minister of Portugal publish anti-Jesuit propaganda in France in 1758? Short answer, he was trying to enlist the Bourbon monarchs (France and Spain) to help suppress the order. Or, why was pro-Jesuit propaganda being published in Nuremberg in 1788? Short answer, Protestants in the Imperial free city could use the story of the Jesuit suppression to censure the Catholic Church for its corruption and politicization. So place of publication helps scholars ask better-informed questions about historical sources.
Assessing modern histories. Sometimes this is just about geographic bias. For example, if I want to read about the Viking-Age Faroes (in the North Sea), my best bet is a history published in Edinburgh, Scotland. But if I want to read about Finland, I'll probably look at a history published in Stockholm, Sweden. Sometimes this is about scholarly trends in a countries university system. For example, if I want to look at power relations and networks, the landscape archaeology of Sweden is a good bet. But if I want to look at perceptions or the experience of the landscape, then the landscape archaeology of England is a good choice. So if I already have specific questions and I'm working with a large bibliography, knowing place of publication can help me figure out where to start.
Plus, as others have noted, it can help track down an exact source. This is especially true if you're trying to track down a page citation from a text that's appeared in many different editions.
Some of this demand can be attributed to historians' penchant for OCD behavior. The preferred style for academic historians is Chicago-Turabian, the latter part stems from Kate Turabian who codified the various standards.
However, the value of listing a city is also because not every edition/printing of the book is the same. Publishers change and newer editions may have additional material or different page numbers and it's vital for fellow scholars to be able to tell what edition your paper uses. The city is a vital clue for this, especially since publishers can come and go or amalgamate.
I would argue that it is not necessarily an artifact. I recently encountered two seemingly identical versions of a book. One book had an error that the other had rectified. One was printed in New York the other in Hong Kong.
I'd agree it's an artifact. More significant in a time when publishing/printing were indistinguishable (or performed proximately). Now, the mere location of some corporate head office doesn't imply as much about where the intellectual or material product was made.
Still, hardly surprising that conventions outlive utility. Something like this is but a drop in the ocean of time/ink "wasted" on addressing--where a correct postal (ZIP) code makes city/state redundant.
Tradition is a powerful thing. Many outlive utility. Some outlive even comprehension of their original purpose.
To agree with the other posters here, it's a requirement that is less relevant for modern books, but is sometimes helpful for older books that have gone through many editions, where there may be page numbers or even entire chapters that differ greatly between different editions. In the age before electronic typesetting, page numbers could differ quite a lot between different printings of the same work, and so city of publication could be helpful in tracking down an exact page citation.