I find three definitions of surgery in Merriam-Webster's Eleventh Collegiate Dictionary (2003) for which the plural surgeries seems eminently reasonable:
3 a Brit : a physician's or dentist's office b : a room or area where surgery is performed 4 [...] b : OPERATION
That a room where physicians receive and examine or operate on patients may be called "a surgery" and that multiple such rooms may be called "surgeries" seem unexceptionable to me. An entry for "a surgery" appears in John Kersey, A New English Dictionary, eighth edition (1772):
A Surgery, a place or room where a surgeon performs his operations.
And Rowland Jackson, A Physical Dissertation on Drowning (1746) gives this instance of the phrase in action:
The Surgeons of the Town having obtained his Body, in order to make a Skeleton, brought it into a Surgery, where they left it upon a Table ; but when they came next Day to dissect: it, they were surprized to find the Man not only alive, but in good Health, and pissing in the Chimney for want, as he said, of a Chamber-pot.
Definition 4b of surgery (the single word "OPERATION") is presumably a more hotly disputed case. And yet that definition has been appearing in editions of the Merriam-Webster Collegiate series for more than 50 years—since the Seventh Edition (1963).
A Google Books search finds this early instance from John Aitken, Systematic Elements of the Theory and Practice of Surgery (1779):
Spina ventosa indicates a Surgery nearly similar to that proposed for Caries [chapter reference omitted]. Trepanation may produce the most salutary effects before the lamellated portion of the Bone be eroded.
Here, "a Surgery" seems to mean "a form of surgery." But it could just as well mean "an operation." And in this example, from Russell Trall, The Hydropathic Encyclopedia: A System of Hydropathy and Hygiene (1853):
DROPSY OF THE SPINE.—This affection is mostly congenital ; it consists of a soft fluctuating tumor on the spine, from fluid accumulated within the coats of the spinal cord, protruding externally in consequence of some portion of the vertebral column being defective. It is generally fatal, although a cure has taken place spontaneously in a few instances, and several cases have been reported as cured by repeatedly puncturing the sac with a fine needle. With the exception of this surgery, if deemed advisable, the proper course is to attend to the general health, and "trust to nature."
the equivalence between "this surgery" and "this operation" seems clear. Is the phrase "this surgery" less offensive to some sensitive persons' ears than "a surgery" is? I wouldn't be surprised if that proved to be the case—and if it did, it seems to me, instances of "this surgery" might have acted as the advance party of Achaeans entering the city and then unlocking it to the subsequent depredations of "a surgery."
An Ngram chart of "a surgery" (blue line) versus "this surgery" (red line) for the period 1700–2000 suggests that "a surgery" broke out of its fairly stable frequency between the 1870s and the 1930s when "this surgery began its steep ascent during the 1940s:
As the chart indicates, despite the rapid increase in frequency of "a surgery" since about 1970, the frequency of "this surgery" has grown at an even faster rate. The plural form surgeries (green line), meanwhile, has dwarfed both "a surgery" and "this surgery" in frequency, again starting around 1970:
And interestingly, whereas recent instances in the Google Books search results for "a surgery" skew heavily toward instances where "a surgery" is followed by a noun such as "room" or "center," many recent examples of "surgeries" clearly use it in the sense of "operations"—in constructions such as "vascular surgeries are frequent features..." and "By clustering surgeries with similar duration variability characteristics..." and "adverse event rates among glaucoma surgeries..."
It thus appears that dissatisfaction with "a surgery" may be somewhat misdirected, since the terms "this surgery" and "surgeries" show up much more frequently in the Google Books database in the reprehended sense of "operation[s]" than "a surgery" does.