Not 100% on this but I'm pretty sure that the NFL included this as a part of the exclusive contract. NFL doesn't want the "tattooed" image on the video game. Like I said I'm not totally sure this is the reason but this is what I've heard.
Not true. I still play Madden 05 and 06 (06 is when EA got the exclusive license) on PS2 and both games have players with tattoos. Although the tattoos are quite basic (one on each arm), the one player they have right is Brian Urlacher's small band tattoo.