My3sons
The public schools seem to dominate according to the IHSA website:
Class AA
Most Appearances
STATE FINAL TOURNAMENT
CLASS AA: 11, Edwardsville (H.S.), 1980, 82, 88, 90, 91, 98, 99, 2000, 02, 04, 07
10, Oak Park (O.P.-River Forest), 1981, 84, 85, 86, 90, 91, 95, 98, 2001, 2005
8, Chicago (Clemente), 1979, 81, 82, 88, 89, 95, 97, 2002
8, Winnetka (New Trier), 1980, 83 (East), 1989 (New Trier), 1993, 97, 99, 2000, 2002
8, Joliet (Catholic), 1977, 1980, 81, 88, 90, 94, 2000, 2004
8, Barrington, 1980, 86, 87, 88, 95, 98, 2005, 07
7, Bartonville (Limestone), 1979, 80, 81, 2001, 02, 05, 06
6, Tinley Park (Andrew), 1989, 92, 97, 98, 99, 2002
6, Belleville (East), 1978, 85, 86, 87, 96, 2003
6, Lockport (Twp.), 1963, 1984, 92, 97, 98, 2005
5, Chicago (Simeon), 1983, 85, 90, 98, 99
5, Springfield (Griffin), 1982, 87, 88, 89, (Sacred Heart-Griffin), 2005
5, LaGrange (Lyons), 1987, 1996, 2001, 2003, 2006
4, Oak Forest, 1979, 80, 85, 86
4, Belleville (West), 1984, 92, 93, 97
4, Chicago (Lane), 1994, 96, 2000, 01
4, Mundelein (Carmel), 1990, 94, 99, 2004
Since 2000, catholic schools have won only one class AA title 2004 Notre Dame (Niles)
2000 New Treir
2001 Bradley
2002 Orland Park
2003 Lyons
2004 ND
2005 Lockport
2006 Illinois Valley Central
2007 Neuqua Valley
Apparently the public schools do very well. It is not right to diminish the hard work of public and private school athletes with this discussion. The facts dispute your claims.