As a language teacher, it pains me to see the rules in D&D for languages.
But, it's one of those things that looks fantastic on paper but, really sucks in play. Doing charades and whatnot is fun for a session or two. After the third session, it's a drag. After the fifteenth session where you yet again have to mime everything out to try to get things from the NPC, and most people are ready to throttle the DM.
Yes, every group should have a language. Those languages should take years to master. Hell, ask anyone who's tried to learn to read Japanese or Chinese and watch their eyes roll up into their heads.

Never minding every species has a language as well. How many dwarven, elven, orcish, goblinish, giant, etc. langauges should the setting have?
At some point, it stops being much fun.