I'll give you my novice opinion.
Cooks is a deep threat because of his speed. Most of Cooks' receptions last year were from quick routes. Slants, out routes etc...
The addition of Cooks creates coverage problems for opposing defenses.
Anyways I expect the addition of Cooks will create matchup problems for opposing defenses.
For example: (Using man to man in this scenario)
Opposing defenses 2016:
Edelman = # CB 1 (Best Corner)
Gronk = Strong Safety or Sam LB
Mitchel = #2 CB
Hogan = #3 CB
Amendola = # 4 CB
Opposing defenses 2017:
Cooks = #1 CB
Edelman = # CB 2
Gronk = Strong Safety or Sam LB
Mitchel = #3 CB
Hogan = #4 CB
In other words he will force the defense to shift their coverages which will cause greater matchup issues. Which is exactly what Brady does best. Finds matchup problems pre snap.
Anyways the Pats won a SB without Gronk a few months ago who is one of the leagues best blocking TE's. Btw so is Allen. Not sure where your worries are coming from. The addition of Cooks and the return of Gronk is something to be excited about. Really.
And yes Cooks will occasionally go deep.
Have a feeling we're going to see a lot of 3 and 4 receiver sets this season. Plus Gronk. Plus White or Lewis or Gillislee and maybe some Burkhead.
How you are finding away to crap your pants about the season with this roster is beyond me. (I say that in a friendly joking way)