You're overstating Grier's control... Grier may have had final say but Wasynczuk and Carroll were involved in the process. You're saying Carroll had literally zero input with personnel decisions... again, that's an overstatement.
Carroll was the antithesis of Parcells and part of that was being less demanding and more tolerant... he was aiming for a more amicable relationship with his players. A consequence of that was declining discipline for sure... the disorganized state of team I'll take your word for it. I'll still insist it was the undisciplined play of Bledsoe that led to the downfall of the team on the field. When you throw 17 INTs in 8 games, your team will lose a majority of them, which they did.
I think you're being a little inconsistent in your complete criticism of Carroll, essentially blaming him entirely for the decline of the team, when you and others are pointing out how bad Grier was with the roster construction. Certainly the poor drafts alone were weighing the team down some. And again, the quarterback play was an albatross.
Also, how do you explain the team getting worse with Belichick as the head coach in 2000? 5-11, then 5-13 through the start of the 2001 season until Brady took over as the starting quarterback.