The reason is Great Park is managed by the City of Irvine. There is no league agreements to be had. The try to be Fair to everyone. But mostly only serve Irvine based clubs with residency requirements. SCDSL and CSL would love to have an agreement with the Great Park. They (City of Irvine) won't do it.
Silverlakes and So Cal will make agreements to fill their complex. They prefer to rent large amounts of field space, not one offs like the Great Park.
You sure about that part?
I'm sure Blues, Slammers, Pats and West Coast have some Irvine players on their rosters. But not enough to satisfy what most cities require for residency requirements.