Ty and Lawyer were part of the culture Bill had to change when he came here. They bought in initially, as did Tedy and Willie and Troy and Adam and several veterans Bill needed to win over to sell his way and system. But once the first ring was in hand Lawyer started to revert to the guy who wanted to bask in the glow of success. He cautioned others to get your credit (pro bowls, money) and make sure that talent got the credit over system. Ty and the others were not vocal clubhouse leaders like Lawyer and generally kept their own counsel, so while a couple of them had similar mindsets they didn't effect the culture like Milloy was starting to. That is why he had to go early on. He wasn't focused on the same singleminded goal of winning championships.
Eventually Ty and Adam and Willie had enough rings and while they didn't undermine Bill they just wanted theirs, here or elsewhere. And in ty's case wanted not just money but a chance to prove he was more than a product of a system. Wanted to be courted by some HC/GM. Bill doesn't court. He doesn't publicly fawn or even allow his players to portray him as fawning. He doesn't make promises he may not be able to keep just to reel you in. Other organizations do or at least have no issue with players portraying themselves as special...
Troy and Tedy in the end were the only two holdovers who truly bought all in. Luckily for Bill he found a couple of others in Brady, Harrison and Vrabel who more than made up for the others opting out. Welker was born all in...Randy seems to have bought in although he did get his finances covered...
Richard has never been all in. He was raised by Lawyer. He's kind of conflicted in wanting it all (money, laurels, rings). Hopefully some of the younger starters like Warren and Wilfork and even Mayo will be all in guys. Asante was never in, which is why Bill let him go and loves Hobbs - he plays hurt and with abandon that belies a guy who has not yet gotten his (financially).
Ty and Lawyer were my boys back in the late 90's. They seldom let me down on the field. Off it, crashing disappointments and therefore dead to me. I don't feel that way about AV or Willie because I don't think they had nearly the choices. 'Sante and Meion are also dead to me because I think they both got way more than they earned out of their brief mid dynasty soujourn here and it was always just about getting theirs for those two.