The Patriots in 2007 had the most prolific deep threat in NFL history in Randy Moss, who broke the all team record for regular season TD's.
That did not stop the Pats from struggling in multiple games in the playoffs that year, including the Superbowl.
Multiple posters here have noted that in the last 7 years the Patriot offense has lost big playoff games in which the offense has put up 17 or fewer points, especially by getting shut out in the 2nd half or in the 4th quarter of games.
The solution to this is not throwing money at a stud wide out. At best it would just be 2007 all over again, and will not address the original core problem(s) that result in offensive choke jobs.
The solution is looking at something a poster pointed out about Game Preparation Theory, in which playoff teams catch up to the K-Gun Patriots after more comprehensive playoff scouting.
The Patriots need to scout themselves especially on offense, in order to understand how to beat teams that make various 2nd half adjustments on them. It is NOT a talent issue, it is a play calling issue. In 2001 the Patriots had terrible receivers, but called the right play to secure the key 3rd down or make the key catch to advance a game-winning drive.