Every year, a cluster of vested veterans (i.e., players with four or more years of service) are unsigned before Week One because the base salary of every vested veteran who appears on a Week One roster becomes, as a practical matter, guaranteed. After Week One, some of those players are signed, since their base salaries at that point aren’t guaranteed.
But the race to sign them doesn’t begin when the last game of Week One has concluded. It starts when each team has concluded its first game of the season. This gives the teams that play on Thursday night a head start of more than two-and-a-half days to get those players under contract.
In all fairness, the trigger should be the same for all teams. But two teams won’t be complaining about it this year, if they’re hoping to sign one or more of those available vested veterans -- the Vikings and the Saints.