Looking at LB's:
Fletcher was a ST favorite, and occasional back-up in the coverage ILB role perfected by Roman Phifer.
That list includes:
Darius Fleming - ST player, has speed and some starting experience, with the Pats much of last year.
Chris White - ST leader the past couple seasons
Jonathan Freeny - ST leader targeted early in free agency
Dekoda Watson - another ST linebacker, blazing speed at 4.40 40-yard dash, but limited defensive capabilities
Matt Wells - drafted relatively high for a ST player, an undersized speedy ST linebacker
Fletcher would be in this soup. I can't see any reason to add him. One could make an argument for every name on that list. However, last year the Patriots opened with only five LB's; the year before it was seven. There are usually two or three ST linebackers each season.
One thing that pops out - Freeny signed early in free agency as a compensation-related pick, with a $1mm salary. That is, the Patriots would lose a potential compensatory pick. None of the others cost a pick; none of the others would that much salary.