Why should she leave? If Cadence could carry the title of Princess and be a babysitter, I'm pretty sure Twilight could be a librarian a while longer. After all, she's not ready to lead a country, she still has a lot to learn. This is just a step towards that destiny.
...but Cadence was babysitting Twilight before becoming Celestia's student. Note that she doesn't have her cutie mark in flashbacks. So unless if you're suggesting Twilight's parents were nobles long before then...
Why would she only foal-sit noble kids? Everything about Celestia's actions practically screams that she objects to the frou frou high-class interpretations of princesses: from anticipating the destruction of the gala [Best Night Ever], to attending the Running of the Leaves [Fall Weather Friends.] Heck, the fact that Twilight seems to know absolutely nothing about how to act around the high class whatsoever [Sweet And Elite] just goes to show the Celestia isn't even trying to integrate her into that crowd despite knowing the path Twilight would eventually go down. Considering Cadance lived in Canterlot and probably was influenced by Celestia, I doubt she'd associate with them either.
Well, Twilight's ascension to greater things means she has many more duties, around equestria, lowering her contact with her friends. Given that she is moving to greater things, it is safe to assume the rest of the group will as well. The best analogy i can think of is when a character in D&D reaches the 10th level and goes paragon, moving on to things that are much more important and difficult, the rest of the party tends to follow suit. Chances are the rest of the group will become even more significant figures in equestria's history. Presumably the next season will be focused around ascension and having to understand when to let go, and when not. Chances are the end of season 4 will be wrapped up with a film, and season 5, if there is one, will be about the descendants of the mane six.
Well, considering Twilight needs her friends to wield the Elements of Harmony, they're pretty much tied to her for the time being. Heck, she brings them along every time she leaves Ponyville, I don't see why she won't do that in future royal business trips.