Bill clearly drafted well in the 2001-2005 era: Seymour, Light, Branch, Givens, Graham, Jarvis Green, Ty Warren, Eugene Wilson, Asante Samuel, Koppen, Tully Banta-Cain (ST player is fine outcome for the ass end of 7th round), Wilfork, Ben Watson, Logan Mankins, even Ellis Hobbs and Nick Kaczur and Matt Casell (a top 5% outcome for a 7th rounder). That is a great haul, and it not only accounted for the first 3 Lombardis, but also helped extend the playoff contention window well past beyond what most thought possible. Yeah, that one draft pick from 2000 helped, as did Bill's acumen. But, still, there is no counterargument to the one that Bill drafted exceedingly well in that period.
And, to be fair, Bill also benefited from players drafted before he arrived: Ty Law, Willie McGinest, Lawyer Milloy, Troy Brown, Tedy Bruschi and Ted Johnson in particular. But he also had to bring in an entire offensive line (besides Damien Woody) and interior DL and LB corps (above players aside) in 2001 to make the team competitive.
There was a definite draft day dry spell starting in 2006 that lasted until about 2010 (existing head coach excepted), when he selected McCourty, Gronk, and Hernandez. The next few drafts brought in Chandler Jones, Hightower, Jamie Collins, Nate Solder, James White, which allowed Bill to renew the window all the way through 2018. But the drafts were meh since 2017 (albeit some special circumstances there with GFIN trades), and those chickens came home to roost once Brady decided he needed a change.
Bill, like every single GM in the NFL, past and present, made mistakes. But those draft hits did a lot to cover up his mistakes. And, like with every other GM, once those hits disappear, so do the job prospects with the current employer.