Your position used to make sense as a 'style', especially in a salary capped league. However, given that the team hasn't won the Super Bowl since 2004, it no longer does. The problem with being a hardass (I'm not debating that there are good things about it, I'm just pointing out the problem aspect at the moment) is that you will lose players that you thought you could afford to, only to find out that you couldn't get adequate replacements, and hosed yourself as a result. It's really not surprising that the only time since 2004 that the team has been back to the Super Bowl is in the year where the team took a risk and made a big jump into the pool with guys like Stallworth, Moss and Welker, because the team seems to have failed to adjust with the times when it comes to dealing with its own high-end players.
It's not the player you lose that kills you. It's the player you don't adequately replace. When the team ditched Milloy, they had Harrison waiting and got lucky with Chung. That's not always been the case, though, and that seems to have become a bit of a blind spot for the organization. You can't be ditching Asante Samuel, replacing him with Deltha O'Neal, and expecting everything to work out just because you're Bill Belichick.