I think few people grasp that the "Mayo error" and Wolf having a really bad free agency cycle and draft, and then Vrabel coming on board and suddenly the draft and free agency are home runs, are not a coincidence.
Wolf holds some responsibility, but I have to guess it was very hard to sell free agents on the idea of playing for Mayo who very clearly had no idea what he was doing, to come move to Foxboro and pay higher taxes as well. It also seemed like Kraft may not have wanted to go "all in" with the cash for Mayo like he was for Vrabel who was more of a sure bet. In the draft, there's also a relationship - the front office needs to know what types of players to target from a scheme/personality fit standpoint, and I am sure Mayo was not giving much or any feedback in that regard, so Wolf was likely left to just wing it and clearly was reaching to draft for need, which as we know didn't work out.
It's not necessarily that Vrabel and Cowden magically taught Wolf how to do his job (although I am sure there was some level of that) but also that they actually allowed the team to become a marketable destination and helped guide the front office on what to target so everyone was operating in sync.