One correct fact... SOME state do separate privates from publics, but probably not for the reason you are trying to support. If you look at the FULL field of teams throughout the states, the privates are not dominant.
It was a cultural shift for me to examine other states and their stance on Privates vs Publics. I was awakened to this California-centristic view. California tends to be a minority in this viewpoint. For example, Texas tends to lean heavily toward publics vs privates. In fact you have to dip al the way down to #85 in the Texas list to find a private on the Calpreps 2003-2020 Dynasty ranking to find the first Private.
Other states on that dynasty list for the highest Private (i think I got all the first privates, but I reserve the possibility a very few errors):
AL - #14
AK #26 of 31 teams
AZ #7
AR #17
CO #1 and then #7
CT # 7
DE #6
DC #1 ( and a very low ranked #1, reminding me of our SFS section)
FL #1 (IMG, a cheater by some standards), #2, #19
GA #35
HI #1, #18
ID #7
IL #1, #6
IN #4
IA #4
KS #1
LA #1
ME #2
MD #1
MA #2
MI #3
MS #7
MO #4
MT #1
NE #2
NV #1, #10
NH #4
NJ #1-4
NM #27
NY #1, #5
NC #25
ND #8
OH #1, #3-#5
OK #9
OR #1, #3
PA #1, #6
RI #1, #3
SC #92
SD #15
TN #2-#3
TX (See Above)
UT #29
VT #5
WA #5
WV #13
WI #6
WY #58 of 58
If you really want a take away regarding Publics vs Privates, its the liberal states that tend to have a dominance in Privates and the conservative states that have a dominance in Publics.