Hey, I know about this stuff!
Bledsoe was ready to play by the last few games of that season, but Belichick declined to put him in. He spelled Brady (and did a good job) for part of the playoff victory over the Steelers, but again Belichick chose to start the unproven Brady in the Super Bowl against the Rams. Bledsoe swallowed hard over the decision, but had no choice.
There's a book about that season and the following two written by a Boston sportswriter. I cannot remember the title, but he quotes Belichick as stating that Bledsoe had too many liabilities.
The best evidence is this: NE traded him to a division rival (Buffalo.) They were well aware of Drew's weaknesses and weren't scared of him. You don't normally trade "good" quarterbacks to division rivals. There were other teams which showed interest in obtaining Drew at that time.
Bledsoe, in my opinion, had hurt the NE Patriots many times while serving as the starter. I was happy to see him go. He has a few good games in a row then stinks up the joint for several other games. Otherwise, he's a friendly and cooperative player.