Cooks was productive but he's not the type of WR who can take over a game. He disappears for long stretches and doesn't handle contact very well. He's obviously a burner, but even with his top-end speed, he doesn't track the ball well on long throws the way a typical deep threat would. He was deadly on those WR sweeps inside the 10-yard line, and a nice piece to have in your offense. But he wasn't a dominant, bonafide #1 receiver, and will probably get paid like one after this year is up.
This isn't a case of my mind changing about a player that my team traded. I would have given the same assessment of Cook at this time last year. I happened to own him for two seasons in a FF league with keepers, so I followed his production pretty closely with New Orleans. A lot of times he was a feast or famine guy. That continued last year in NE.
I read that he'll probably get around $14M/season when his deal is up. Maybe LA tries to extend him, I don't know. But there's no way the Patriots would pay top dollar in this case.
So, they dealt him when they were able to sell high.
Their 1st rounders, by formula, could get them as high as pick #9. They have two seconds as well (SF's and their own) so there's a chance BB moves up. But I doubt they'd go all in and trade three (or even 4) picks in the first two rounds to get just one guy. They need some youth. And they only drafted 4 (IIRC) players last year, not all of whom are still around.