[Zigûr]

Originally Posted by Eäralda Halatiriva

aren't both of them serving Eru, whatever they might choose to do?

An excellent point, and one I'd neglected. To quote Eru in the Ainulindalë:

And thou, Melkor, shalt see that no theme may be played that hath not its uttermost source in me, nor can any alter the music in my despite. For he that attempteth this shall prove but mine instrument in the devising of things more wonderful, which he himself hath not imagined.

In regards to language, I thought I might offer this point in Appendix F:

It is said that the Black Speech was devised by Sauron in the Dark Years, and that he desired to make it the language of all those that served him, but he failed in that purpose.

It could be in this case that the desire for a single unified language for all his subjects derived from Sauron's desire for order and efficiency; it would certainly have aided communication. We can imagine, perhaps, that like Orwell's Newspeak its vocabulary might have limited the capacity for "disordered", which is to say rebellious, thinking among Sauron's slaves.
As for Morgoth, I know Professor Tolkien mused upon but ultimately rejected the idea of "Melkian" languages from which the Black Speech and other dark tongues derived, but what strikes me most about Morgoth is how often he is described as a liar, and a liar to himself as well as to others. From Valaquenta:

Understanding he turned to subtlety in perverting to his own will all that he would use, until he became a liar without shame.

In terms of knowledge production it's worth noting that it was a two-person job for the dark powers: Sauron "was often able to achieve things, first conceived by Melkor, which his master did not or could not complete in the furious haste of his malice."
Just a few ideas that might be relevant.