I can think of several reasons.
One would be tradition. "My master taught me in Enochian, so I use Enochian. Besides, it really isn't worth the effort of doing a wholesale translation on all my books. Sometimes I find one written in Sumerian or Khemetan. I can read those languages - mostly - but it's still better for everyone involved if I just take the couple days and put them into Enochian, just to make sure I don't accidentally summon a demon. Even then, I can sometimes get away with a few Enochian notes in the margin."
To take a cue from real-world religion, it's sometimes about power. The Romans wanted the Bible kept in Latin, even though the language was dead, because it kept the knowledge/power exclusive. Why spend a spell slot to do something, when you can use someone's imagination about what you could do against them? Sure, you sometimes get a John Hess or Martin Luther, but those cases tend to get "handled" such that even sympathizers keep quiet.
Magic is dangerous and, whether at an individual or organizational level, you tend to run into unsavory sorts. Even if you trust your apprentice, milk maid, guards, etc. These stupid adventurers have no qualms about being hired to break in and steal your stuff. Well, if it's coded, it's less appealing to randomly kill you and steal it (unless everyone uses a code, but then it's a matter of not being the one idiot without a firewall). Also, assuming you aren't killed in the process of stealing your secrets, it makes it harder for your secrets to be used against you.
Real world languages tend to express different concepts better than others. I tend to think that one reason why there were so many great Greek philosophers is that Ancient Greek lent itself well to describing such things. Whether Common is a pidgin tongue or just the native tongue of whatever nation is currently "on top", it may not be the best for expressing the subtle differences between setting your enemy on fire and setting yourself on fire ("Hey, did you know the only difference between 'ten feet in front of me' and 'in my pants' in Common is an accent mark on the 'a' sound?").