Nope, not the only reason.
LINEBACKER HELL 2005-2007
Analyze 2005, 2006, 2007 and 2008. Law would have helped, but the defense needed even more than that: fewer injuries, flu shots, and linebacker improvement from the 2004 draft onward.
With McGinist (and Phifer) aging and almost ready to go, how did we prepare in 2004 and 2005? We added no one in 2004. Were unprepared when Bruschi and Phifer went down and out respectively in 2005, and brought in Beisel and Chad Brown. Where were the youngsters; where was the depth on the team? Hey, we drafted Claridge in 2005. 2005 and 2006 was the year when linebacker became a severe weakness. Finally in 2007, we brought in Thomas (and Moss and Welker). Was he really enough? Yes, enough for a perfect season, but not enough for the future. Who were we developing? Well, Woods was a 2006 UDFA who we had in place of Tully the 7th rounder and we drafted Lua. BFD!
FINALLY, in 2008, Belichick paid attention to bringing in linebackers. He brought in Mayo, Crable, Guyton, Redd, Robertson and Ruud. Woods had indeed developed enough to replace the aging and slowing Vrabel for 2009, with the help of an old collegue Tully.
And yes, in 2008 and 2009, Belichick replaced all the corners and added a few safeties to youngsters James Sanders and Meriweather.
No, Law wasn't the only reason for not winning a Super Bowl after being one of the best teams of all time in the 2003 and 2004 seasons, but the depletion of the secondary was certainly one of the primary factors along with the linebackers.
Yeah idiot the only reason we haven't won any superbowls is because Law left.