Use of the fullback position really is dying, and the elite ones are pretty poor value because of that. Last season, Leach had a $4.3M cap number to play 42% of their offensive snaps. He had the same cap number this coming season. That's really poor value, and it's why he ended up getting cut.
For comparison, Marcel Reece played the highest percentage of all FBs with 61%, and he's a converted college wide receiver who has a lot of value as a receiver and was also a primary ball-carrier for four games. The only other fullback above 50% was James Casey, who is now listed as a TE with the Eagles. The top fullbacks in playing time aren't blockers, they're receivers.
So let's say the Patriots could sign Leach for $3M a year. That's quite a bit less than what he was making with the Ravens, but more than the $2.5M per year the Vikings just gave Jerome Felton (who played only 38% of the snaps last season). What percentage of the offensive snaps do you expect a guy to play for $3M a season? For that kind of money, I'd at least expect him to at least be around the 60% snap mark (which would put him in contention for the NFL FB snap lead), and I wouldn't be able to rationalize having a one-dimensional run-blocker on the field even half that often.
Belichick has the right idea when it comes to the fullback position. If you're a passing or even balanced team, you don't need a real fullback. If you're going to have a fullback anyway, then he needs to be a primary ST player. He'll get about as much use on STs as he does on offense. He also needs to come cheap, about a million or under. And if you don't want a real fullback, then tight ends, linebackers, and offensive linemen work too. And no matter which player you pick, you're not paying a guy $3M to sit on the bench for 2/3 of your snaps.
[Now Marcel Reece, unlike any other fullback, I'd take for $3M a year in an instant. He's probably the closest player in the NFL to having Hernandez's movement skills and oversized receiver body, but with more ability to play as a running back (both halfback and fullback) than Hernandez. The Patriots would do amazing things with him.]
tl;dr: Highly paid fullbacks are crappy value.