The entire California university system, both historically and presently, is structured around high school class rank. As originally conceived, the concept was that the top 10% of graduates would be eligible to attend UC’s, whereas those who weren’t at that level would attend CSUs or community colleges. There have been numerous tweaks over the years - now it has tightened to top 9% - but class rank remains a significant factor, both on a per-school basis (“local context”) and on the “statewide path.”. The ranking is determined by measuring GPA in only specific, UC-approved and required coursework. So the system is specifically designed around the idea that California high schools are direct feeders into the University system.
Of course out-of-state students and homeschoolers are admitted, but they are coming in via an alternate path with no guarantees. Homeschoolers can be eligible for the statewide path if the complete the requisite A-G coursework, but tha isn’t just a matter of attaching a title to a home-studied subject - because the coursework has to be approved, the homeschooled student would need to work through an approved on-line course provider or local charter in order to complete the coursework.
I think for many homeschoolers the better path would be California’s guaranteed transfer via the community colleges. The student who completes the requisite CC courses along with the required GPA can qualify for guaranteed admission to most (but not all) UC campuses. So that is the route that enables homeschoolers to essentially get on track for UC admissions.
I think realistically most homeschoolers with strong test scores will also be admitted as freshmen to the less popular campuses – UC Santa Cruz has close to a 60% acceptance rate overall, Riverside is 66%, Merced is almost 75% – and all of those campuses are going to be very happy to take in a student with scores like the OP’s son.