Nikola reports that you get a huge discount, nearly 50% off, if you do the following:
(a) Select the haircut online from a list (like this one),
(b) Reserve a time for the appointment,
(c) Select a stylist(?), and
(d) Pay online.
All of this amounts to "buying the haircut online". In effect, you are given a huge surcharge if you don't.
I can see some benefits to this: The hair-cutter who meets the client can be a specialist in the particular style she wants (I guess); time-efficiency is maximized because the stylists do not need to just sit around the workplace at all hours waiting, and would only need to come during the appointed times; no one needs to answer the phone to create these appointments, since it's done online; plus no one needs to handle money or payments transactions, as that's also online; nobody even needs to go through lengthy explanations or discussions about how to style the hair, because the stylist can see what the customer wants via the selected pictures, so yet more time/energy are saved....
Yes, it seems like an efficient system. A bit surreal, or unsettling, to pick a style online. I've never even gotten a haircut in which I asked for a particular style. The $6-per-haircut I pay does not qualify me for "styling". I don't mind. It's just a haircut.
The author of the blog I link to above is Nikola, of Croatian origin but a German citizen (from what I gather) who is studying in Korea and speaks (at least) Croatian, English, Korean (passably), and German, the latter of which is most comfortable and is the language of his blog.
Hits on Google
Zero (0) for "buying a haircut online"
Zero (0) for "buying a hairstyle online"
Zero (0) for "selecting a haircut online"
One (1) for "selecting a hairstyle online" [but the site seems to be a spam-site]
One (1) for "choosing a haircut online" [obviously generated by a spam-program from the context]
Two (2) for "choosing a hairstyle online" [both possible spam-sites]
19 (nineteen) for "buy a haircut online" [none of which allude to the concept Nikola describes]
Zero (0) for "buy a hairstyle online"
Zero (0) for "select a haircut online"
Zero (0) for "select a hairstyle online"
Zero (0) for "choose a haircut online"
Fourteen (14) for "choose a hairstyle online" [most are obvious spam-sites, only this one is a real, definite human usage of the phrase, and it is not connected with the concept Nikola describes]
I conclude that the concept of "buying a haircut online", as described above, may be unknown to the English-speaking world.