Audio Clutter.
Music with lyrics have to be implemented very carefully. It is very easy to overload the sensory and concentration of a player if you've got other stuff going on like lyrical background music. For example: It's very hard to read text and listen to your music at the same time. This can even be frustrating to a player who might just turn off the music entirely (if it's an option) in order to be able to read the text without being distracted. Another example is that it's hard to concentrate on lyrical music when you've got an action scene going on and you've got other sound effects that might drown it out (or the music drowns out the sound effects).
Often, the point of lyrics in any music for a game or a movie is to try to convey the feeling or emotion of the situation without using words. The effect this tends to have on people is a compelling emotional experience in which the audience doesn't need to be told what's going on, because the song tells you absolutely everything you need to know.
Let's look at a fantastic example.
1000 Words. This comes from Final Fantasy X-2. Yes, it's a really stupid and terrible game. However, if you managed to play it up to the point where the title character Yuna sings it, it tells you everything you need to know about the situation. It doesn't just tell you about the relationship between Yuna and Tidus, but also their "look alike past lives" that the story centers around. Everything about that scene with that music makes it a fantastic example for why you would use it and how effective it can be.
Want another example from a different Final Fantasy game? Eyes On Me from Final Fantasy 8. There are grown men who cry to that song when it appears in the game because of how emotional and moving it is. Personally, I don't like the song, but it is a powerful force none-the-less.
Okay, let's go with my personal favorite example from yet another Final Fantasy game (okay, I can't help it, these guys can't design a good FF game, but they somehow manage to nail these lyrical songs with cutscenes and power into our emotions without an issue). Other World from Final Fantasy X. The moments at which this badass rock song kicks in only further cement your emotional state and mentality of "hell yeah!". It makes you feel like you can take on the world and crush any obstacle before you. We get the first glimpse of the song during the Cutscene Blitzball game where Tidus is kicking a lot of ass and making the sport look more awesome than it is in actuality. The song hits its high point when suddenly the city is being destroyed around our protagonist as his eyes open in shock while he falls and missiles streak the air beside and behind him. That song during that scene perfectly sets up the entire storyline of the game as well as what kind of enemy we are going to be facing. Also note, we don't hear this song again until almost the end of the game and it replaces the "Boss Battle Theme" music of the game when we hear it again. During that moment, the song takes on a completely new meaning while still conveying everything it originally did when you first popped the disc into the tray.
So, if you plan to use lyrical music in your game (anywhere in your game, in fact), I suggest you be careful with how you use it and where you put it. You will need to playtest extensively for it. By "extensively", I mean nobody gets to play-test the thing twice because a second listening of the scene/song in question more often than not produces biased feedback (especially since a player on a second go around will know what you're trying to do, and will tell you it works if it's even slightly close). You need to have people experience it and then simply ask "Impressions?". Don't even hint at what you're going for. You need to figure out if you're invoking what you want without tainting the results. If you are at all successful in doing it, you will have one heck of a fantastic game. After all, music is about 30% of a game.
