The film never actually stated that this John Harrison character was Noonien Singh. The character only refers to himself as "Khan", never "Noonien" or "Singh". The only character who refers to him as Noonien Singh in the film is Spock Prime, and Spock Prime was really only talking about the Khan that he knew from his timeline, not having any details about this particular Khan. Remember, "Khan" is a title.
It
can be a title. That doesn't mean it can't be a given name. There are certainly people whose first names are also titles, like the musician Prince (born Prince Rogers Nelson), actor Judge Reinhold, director King Vidor, actor Baron Vaughn, etc.
Besides, if Khan had just been KNS's title rather than part of his name, then he wouldn't have been referred to as "Khan," but as "the Khan." It was consistently used throughout all three of his appearances as a name.
For instance, the Botany Bay was found over 5 years earlier in this timeline than in the Prime one.
Over 8 years, in fact. "Space Seed" was in 2267, and this film mostly takes place in early 2259 judging from the stardate. And Khan was definitely found some months before that.
Anyway, all this just means that the new movie version of Khan doesn’t have to have any connection or correlation with the Khan we’ve seen in prior Trek or the novelverse.
Which rather defeats the purpose of the filmmakers, doesn't it?
The 2 main arguments for being able to ignore long-range beaming and not bring it up in the novels are:
(1) It’s dangerous. The new movie give us yet another example of a successful transport. Just adding to all the other successful transports that we’ve already seen. Against not a single un-successful transport seen. [Scotty beaming into the warp core in ST09 was not a failure of the transport tech, just the coordinates that were being used.] It’s becoming more-and-more difficult to say long-range beaming is significantly risky.
We've seen it used exactly twice -- that's not nearly enough to establish a baseline for its reliability. Even if it failed only one time out of three or four, or even one time out of a hundred, that would hardly be considered a sufficient survival rate to justify putting it into everyday use.
And I would submit that the coordinate error that endangered Scotty was an inseparable part of what makes it dangerous. The greater the distance you have to transport, the more any margin of error is magnified. If you have to beam someone 20,000 kilometers and the position error is one in a hundred billion, then their position will only be off by a fifth of a millimeter, unlikely to be enough to matter. But if you're beaming someone 20 light-years with the identical margin of positional error, then they could arrive anywhere within a volume 95 kilometers in radius! It's the sheer distance that magnifies the risk. The technology would have to be incredibly accurate and glitch-free, given the enormous cost of even the tiniest error.
(We've seen this in other franchises. In the reboot
Battlestar Galactica, we hear about it not being safe to use the hyperspace jump drive beyond the "red line" distance, and the reason for that is that the margin of error increases with distance -- the same percentage error in a much larger number translates to a much larger and more dangerous uncertainty of position.)
(2) It takes a lot of power. This argument was based on Data and La Forge’s description of subspace beaming in “Bloodlines”. But we see in STiD that not much power is really necessary. John Harrison’s ship had no warp drive. And the long-range transporter device that allowed him to go all the way to Qo’noS was small enough to be carried by hand. The amount of power necessary seems a very reasonably small amount—certainly well within the abilities of a normal starship to produce.
Or it could've been a single-shot unit that poured all its power into one use.
Certainly you have a point that transwarp beaming shows the likelihood of becoming a major technology in the Abramsverse pretty soon. But I'm perfectly happy to attribute that to the combined brilliance of Spock Prime and Khan and assume they enabled some additional insight that nobody in the Prime universe has had yet. Sure, if someone wanted to introduce it into the Primeverse novels, it could be justified (as long as the risk were reasonably addressed), but I'm perfectly content to let that breakthrough remain unmade for the foreseeable future.