Do you expect to make the pros?
A school environment gives you so much more than the "technical" skills that you learn in the classroom. It gives you a chance to interact with other kids and teachers. You learn a lot about being a social human being. I thought about sending my kids to the K12 program, but decided that there is too little interaction with other kids and teachers. If you are not in a bad area, and don't have any special needs I would strongly recommend against this path.
The chances you will make the pros are not that high. I don't say this based upon your current or potential skill level, but based upon the number of slots available.
If you join a high school team, the coach (no matter how bad) will spot your talent. You have a chance to play to the CIF level (I remember you mentioned you are in NorCal), and that would be the best way to propel your potential career.
My kid is currently a freshman with a 10-14 hcp trying out for varsity golf, but he doesn't really think he has a chance nor does he care. There are a quite a few sub-5 hcp freshman in his school, so he will be satisfied with JV.
His friend from grade school is also a freshman with a 3hcp, and doesn't think he can make varsity at his school.
There is a lot of competition even at the high school level, and you need to be prepared to pit yourself against your own high school and all the other ones in your state before considering a career as a pro.
I would recommend the standard path for a more rounded education that will give you a plan B.