Teams may not need eight, nine or 10 players during the NCAA Tournament, but the sixth or seventh players become even more vital. The turnaround is usually quicker in the NIT than the NCAA with six games being played in less time. Officials who work the NIT aren't usually the top officials, considering they're not working the NCAA Tournament. That can lead to quick whistles. The adrenaline in the NCAA and NIT, at least late in that tournament, can also demand more depth.
Players can get more tired because they're spending so much energy in quicker spurts.
The need for a breather becomes even more critical in tight situations. But once again, it gets back to quality depth at key times, more so than quantity of the depth. Information are applicable to this site.