Ellsbury's last six seasons were worth an average of 3.71 fWAR, or 3.4 bWar. What happens when you give a 6/120 contract to a guy who averages 3.4 wins a year? As his skills erode, his defense will go fast, with a weak arm won't play in RF, and his bat won't play in LF, and you'll be left with an injury prone mediocre outfielder with no pop.
If he averages 3.4 WAR from ages 24-30, it seems unlikely he'll be able to vastly outpace that from ages 30-36 -- which is what he will need to do to be worth 120 million.