The 'grocery shopping' analogy, if we're gonna use that, is way oversimplified because there are a) multiple chefs in the NFL, b) 'free agent' ingredients are one of a kind, and shop themselves, meaning -they- have to be willing to jump into the pot and be cooked, c) different chefs shop shop for different ingredients because they have different recipes, and d) draft picks are not, shall we say, fully developed ingredients, and require some development/refinement.
And ultimately, in today's NFL, the base of your cooking is the QB, and if you don't hit on the QB, everything else falls on itself and their flaws become much more highlighted.
In lots of ways, Belichick was shopping for years -highlighting- his QB, Brady, as the base of his recipes. Since then, replacing Brady with Jones has proven to be a problem because, ultimately, Jones has proven to be a souffle, where you have to cook just -right- or the whole thing collapses over and over.
If we're carrying the cooking analogy further, I think the biggest problem with Belichick is that his sous chefs the last few years has sucked (Patricia, Judge) and screwed over the souffle (Jones.) His previous sous chef (McDaniels) took a lot of the offense coaches with him, which would seem to indicate lack of continuity, meaning the last couple years has been spent with a bunch of new chefs on offense. In lots of ways, I'm not terribly surprised the defense, which had more continuity on coaching, is cooking better than the offense has.
At this point, if I were Kraft, I'd take a long hard look at the chefs on the offensive side of the ball and consider if the best way to improve the offense is to convince Belichick to hire the chefs O'Brien wants on offense and then shop to -what- that offense wants, and use that time to further work with the heir apparent/sous chef (Jerod Mayo).
I don't think it matters right now, however, who does all the cooking, because the signature dish revolving around the QB basically needs that QB and the rest is just shouting.