All 4 games so far have been won by the home team, and by 1 run, any question about that being an advantage has been answered emphatically here.
The missed check swing call may very well have costs NCST a NC. If I am interpreting correctly, the home team designation goes to the higher ranked team, something that historically favors the SEC.
Apologies again, but this tournament seems to be weighted in favor of the SEC. Check swing calls are totally up to one umpire’s discretion, but not surprising a game ending call was proven incorrect in replay that gave an SEC team extra life.