This is from the Farrar article on the Graham trade in another thread, but it's pertinent here
"The blocking issue could be improved with more reps—according to Pro Football Focus, Graham had 27 pass-blocking snaps in 2014, 4.9% of his 547 total passing snaps"
I'm more interested in the stat than the opinion above. It could be theorized that Graham isn't all that enthused about blocking because he rarely does it. If you're doing something 27 times out of 547, you're typically not as familiar or comfortable with it, and since it's done so rarely, blocking could be a thing he doesn't see as important for him, or just something he has to do a very few times and get it out of the way.
Like Scotte said, it would be a waste of resources to match Graham up on the other team's best edge rusher like we did with Miller. I see Graham as doing more inline blocking. The deadliest part of Millers game (and really and pure TE in our system) is the PA pass, which we obviously do a lot of. Typically the TE will run block and chip the DE, then go out in a route. Against a runner like Lynch it's really difficult for a LBer to watch the TE block down and not believe it's a run. Put Graham into the equation, and you have LBers taking a couple of read steps towards the los, then trying to turn and run with a guy that's running a 4.5 and blowing down the seam. That's where I see Graham doing a ton of damage.
Pete has also said that Graham takes a ton of shots. In speaking to Graham's supposed softness, Pete was mentioning that Graham is getting drilled on literally every play. The coaching staff might try to mitigate that somewhat by limiting his blocking aorund the los. Pete has shown he's really good at managing players and I could see him trying to limit the amount of contact Graham sees in a season by not getting Graham mixed up in the line scrum.
I do think he's fully capable of pasting LBers though.