I have been doing labiaplasty for many years, and the vast majority of my patients prefer local anesthesia. I have the privilege of operating in my own office-based nationally-accredited (AAAASF) surgical facility with full anesthesia capabilities, and a wonderful, talented, and experienced staff of operating room, recovery room, and anesthesia personnel, so I can offer my patients local anesthesia only, local anesthesia with IV sedation, or a full general anesthetic, according to their preferences, anxiety level, and pain threshold. (And cost-consciousness.)
Labiaplasty involves operating on one of those areas of the anatomy that is both perceived and actually is a sensitive area, so some patients will ask for and are willing to pay for a complete anesthetic. But most patients can be truthfully reassured that local anesthesia is both comfortable and complete for labiaplasty, and that careful measuring and marking (along with precise surgical technique) allows me to perform accurate and symmetrical incisions that lead to the degree of labia minora reduction the patient desires.
If there is any erring, it should be on the side of conservatism--you can always take a bit more, but it's impossible to "put back."
Using "improved accuracy" of excision as a reason for utilizing general anesthesia is likely both partly true, and partly surgeon preference, and could be a bit self-serving if the increased cost of utilizing general anesthesia is received by the doctor's own operating facility. It could also reflect a bit of inexperience or personal discomfort with this operation, and a desire to "work out the details" without the patient's awareness!
If the doctor's statement about "tissue swelling" under local anesthesia was true, then s/he must not utilize local anesthesia for blepharoplasty surgery, facelift surgery, or any of the myriad of cosmetic operations that rely on careful measurement, symmetrical incisions, and the beneficial effects of vasoconstrictive local anesthesia (even when the patient is asleep with general anesthesia). So, while true, the statement simply reflects that particular surgeon's preference for general anesthesia with a bit of "justification" thrown in for good measure. (And there's nothing wrong with general anesthesia, other than the infinitesimally-greater risk, the not-so-infinitesimally-greater cost, and a bit of recovery.)
Furthermore, there is an advantage of local anesthesia with adrenaline--more vasoconstriction, less bleeding, less bruising, better healing, and less scarring--which is why we utilize it for eyelids, facelifts, and other cosmetic procedures even when the patient is asleep! So you can see there is actually an advantage of using local anesthesia other than cost-savings.
Bottom line: I don't think I have any problem "artistically shaping" my patients' labia minora under local anesthesia, even while swollen. And in all the years I have been doing labiaplasty, I can recall only doing one revision (taking a bit more tissue per the patient's request). Local anesthesia labiaplasty has not been a problem for me or my patients (or maybe I'm just a better surgeon). See how "easy" it is to be self-serving in our pronouncements that patients take as "fact" when in fact they simply represent habit, preference, or training cloaked in statements designed to look like fact or "science!" Best wishes! Dr. Tholen