The best teams do win in Omaha.
No they don't. They're just as likely to lose or win zero games than they are to win.
The best 20 regular season records (out of 300 teams) since 2008 won 70% of the games in Omaha (108 out of 155).
Significant outliers - The good:
Arizona - 28th best record, 10 wins
UCLA - 30th best record, 9 wins
Significant outliers - The bad:
Louisville - 3rd best record, 1 win
Miami - 10th best record, 2 wins
Teams that held serve:
Virginia - Best record, 12 wins
LSU - 2nd best record, 11 wins
North Carolina - 5th best record, 7 wins
TCU - 6th best record, 11 wins
Vanderbilt - 9th best record, 11 wins
Florida - 11th best record, 11 wins
South Carolina - 13th best record, 15 wins
7 of the 10 national titles went to teams that were in the top 13 for the decade. The ACC is particularly underwhelming in that area, having 5 of the top 10 records, but winning just one title.