The RIAA is against that...they feel you need to pay extra for the lyrics. The RIAA is still stuck in the old world of CDs, where you couldn't display the lyrics even if they were on the CD since the players had no displays.
Sites that offer the lyrics (I use them myself) are often sued by the RIAA just like the sites that offer pirated downloads. The reasoning is the lyric sites get money from advertising on their sites, so the RIAA should get a cut. Plust they consider it piracy.
They could offer songs with lyrics, but they would need to come up with a format to do it - where would the lyrics go? and they would need the companies like Apple and Android and the others to agree on how to store/use the lyrics AND how much more the songs with lyrics would cost.