I don't think it's that at all, I think some veterans (take Mathieu for instance) that are on their 3rd contract, or coming off injuries tend to sign w/ teams after the draft so they can see what their options are. It's a mutual thing, the player has time to get healthier and the team has time to fill it's roster out via the draft and then determine what direction they want to go.
Again, same thing happened with Mathieu after he got cut by Kansas City.