I think TUC's overuse of the quotes...
I know this is veering off-topic, but the strength of TUC in the larger context of Trekdom is its portrayal of a more cultured Klingon rather than the Viking/Samurai stereotype in the TNG-era shows that often veered on caricature with all that grunting and howling and mugs clanking together.
There was somewhat of a breaking of the 4th wall going on by casting a Shakespearean actor to sling Shakespeare as well. Everyone knew who was under Chang's mask, and so it felt fitting to let him quote Shakespeare.
It's also been a Trek tradition to make literary references, all the way back through TOS.
The idea is, at least in Starfleet, that everyone's well-educated in the liberal arts and these things just kind of flow out of them. You saw that again in TNG with Picard quoting Hamlet (one of my favorite TNG moments).
So it's hardly Nick Meyer alone doing this stuff.
Khan's a monster but he's also supposed to be a super-genius, so he is well-read and likes to show it now and then.
Trek has always (at least until JJ) been very preachy which is not unlike Shakespearean drama with all those lofty monologues.