Coach K does not, he is the only big time coach I know that does not. He has lost or been affected in NCAA's by not sitting the guy. At least 2-3 games they have lost in last 15 years in tourney almost all of those were affected by a big or someone else picking up that 3rd in 1st half.
You always sit the guy, any more evidence needed was PJ coming out playing great and UK building 8 point lead with 3 minutes. He picks up 4th at 15 minute mark in second half then that game would be over because Travis would foul out. It is a smart move and only move unless you are getting blown out by 18-20, keeping it close or under 10 or 3 possession game.
He does and he doesn't. Think it depends on the situation. The one I can remember in your timeline is the 2004 UCONN Final Four game when Calhoun parked Okafor and K kept Williams in. Okafor though fouled out three Duke bigs in the second so it probably wouldn't have mattered.
Would be 2 more banners in Durham and Lexington if not for the Huskies.