The real world in a land with dragons, demons, and the like? Where men cast magic with bat guano and words? You mean that real world?
I've already acknowledged that D&D is set in fantasy realms where anything is possible, so you're not adding anything to the discussion.
If we don't liken fantasy settings to the real world except where required, those fantasy worlds become impossible to engage with. If we start to say that air, gravity, physiology, economics etc don't operate the same way as the real world because those realms also contain dragons, demons, magic and so on, it becomes very hard for us to relate to those imaginary places and play games of shared conceptions within them.
There are a lot of people (numerically, if not proportionately) who learn languages at university. One of the more famous in my own country is our former Prime Minister, Kevin Rudd, who is a native English speaker and who became fluent in Mandarin Chinese although he did not study the language prior to university. Of all the people alive today who can read Ancient Greek or Anglo-Saxon or Old Norse, where do you think most of them learned to do so? At University. (I would conjecture that these days that is probably also true for Latin.)
Hence, if wizard college really is a university then there is no reason at all why exotic languages could not be learned there.
I always imagined wizardry, i.e. learning magic, to be a full-time course of study. That's not to say that exotic languages aren't studied at colleges of wizardry, only that doing so is an additional course requiring more time and money. I picture young nobles or the children of wizards having the opportunity, but for the vast majority of new wizard graduates, life gets in the way. So it is possible, just not at all common and hence something players need to justify to their DMs.
In real world countries where speaking two or more languages is common, e.g. Switzerland, the Netherlands and India, those languages tend to be learnt before university age. If the same applied in fantasy realms, all the languages one was ever going to learn would already have been picked up before going to wizard college.
Of course, on both points, those are just my conceptions. There isn't a right or a wrong. Every DM imagines things as they and their players wish.