As I said, I wouldn't even have the phone call conversation at all to establish that Khan is dangerous. That was already done with him taking on a squad of Klingons without a scratch. Apparently to these writers, it's not enough to show that he's a badass, they have to have Old Spock say "oh yes, he's legit!"
The thing about Old Prime saying Khan was "the most dangerous" antagonist is that its unintentionally saying "after you deal with Khan, you'll never encounter an enemy as dangerous!". Really though, I kinda hope there is no villain in the next film. That would actually be refreshing for a Star Trek film. Tons of great Trek stories were told without the need to include some villain. THE VOYAGE HOME was the biggest success of the older films, and that not only had no conventional villain but the only phaser used was to lock a door. That's much more ballsy to pull off in a blockbuster, especially today.
I think you kind of missed the point of this particular scene, especially with the timing of it (in the very next scene with Kirk and Scotty on the vengeance: "I thought he was helping us? / No, I'm pretty sure we're helping him.").
Until now Khan had been playing the victim card, claiming to have been exploited or manipulated or backed into a corner by Admiral Marcus who was the real enemy of the Enterprise and -- to a greater extent -- to all of the Federation. Kirk had even turned to Khan for help in desperation to help take the Vengeance.
For anyone who isn't already familiar with Wrath of Khan (which is to say, all three of my kids, most of my students and my knucklehead cousin who has apparently never seen a good movie in her life) this actually comes as a bit of a revelation: not only does oldspock know who Khan is, he knows his FULL NAME and has fought him before. That, plus Kirk's scene on the Vengeance, foreshadows the revelation that Khan is actually a hell of a lot more dangerous than Marcus; like the Cloud Creature of TOS, it conjures up images of Khan opening up a massive can of whupass on the entire crew and finally being defeated in an epic showdown/battle of wits. Which is more or less what happened; it's just that the details are a lot less interesting than the revelation itself, so the revelation is actually lost on those of us who already know
In that sense, Oldspock sort of represents the perspective of the Veteran Fans: we mostly should have seen this coming, so for us it plays out differently: we know Khan is a crazy super-strong megalomaniac and so we kind of expect him to take the Vengeance on a mission of conquest just like he did with Reliant and Genesis. But for a thirteen-year-old girl who has only ever seen two other Star Trek movies (and only remembers one) and never managed to sit through Space Seed without getting bored, that entire conversation draws an audible "Uh oh..."