A TE who has a relatively modest yards per catch rate, indicating a fair percentage of short balls, should have a percentage catch rate above his QB's completion percentage.
Cook's career 12.8 yds. per catch indicates he's been running a fair amount of short routes over his career.
Lets look at Finley, to take just one example for comparison. While I don't think he was the "bad hands" guy some made him out to be, we wouldn't call him a "good hands" guy either. His career catch rate was 69%. Rodgers completion percentage was 66% for 2008 - 2013, the years Finley played.
The Cook/Finley difference is not great. With Cook about 1% under his QBs and Finley 3% over Rodgers, the 4% differential is 1 catch per 25 targets. In a 90 target season, Finley's high water marks in his 16 game seasons, the difference between Cook and Finley in catch rate vs. QB completion amounts to about 1 catch per 4.5 games, which is negligible.
As a Finley comparable, he fits the bill, with maybe some better run blocking in the bargain if PFF's assessment is accurate.
I like the signing at this price, as I said. It's especially attractive compared to the $7 mil per year Finley was getting at the end. But to think Cook could play meaningfully above his career averages (Pro Bowl some said in these pages) with Rodgers throwing to him is unrealistic. Finley's 2011-2012 averages, his only 16 game seasons, would be a realistic and happy circumstance:
90 targets, 58 catches, 64% catch rate, 717 yds., 12.4 yds. per catch, 5 TDs.