Here is the key to Burkhead. When he is in the game the opposing Defense can't pre-determine it is going to be a run like they can with Blount. Same can be said about White and Lewis. I agree they pick up a big RB in the draft like James Conner of Pitt (6' 1" 233). Burkhead will get the red zone carries and he will play Special Teams too.
When Blount was on the field in 2016, the Pats passed 43% of the time.
In spite of the fact that Blount had almost 75% of all RB carries in 2016, he still posted a 3.9 YPA and scored 18 TDs. He also had seven runs of 19+ yards, including three of 40+. The only other Pats player who had a run of more than 16 yards was Brissett with one for 27.
So, defenses certainly were playing the run when Blount was on the field, but they weren't exactly smothering him. And that really helped the passing game.
BTW - Pats active RBs don't play ST unless they're returning punts or kicks. Blount, Lewis and White combined for a total of 39 ST snaps in 2016. Bolden had 277 ST snaps by himself (and 13 total on offense).
Based on Burkhead's $3.15M contract (more than Blount, Lewis and White made combined in 2016), BB is definitely planning on him being an active RB and won't have him performing double-duty on ST.
While Burkhead does appear to offer more run/pass versatility than Blount (Burkhead had 74 totes to 20 targets in 2016), my guess is that he covers the lead RB role for 200-250 carries, plus 30-40 receiving targets, if Blount doesn't return (even if they draft someone like Conner).
If Blount returns for one more season (still a possibility), I'd guess they split +/- 350 carries between them, similar to Dillon/Maroney in 2006 or Ridley/Blount in 2013.