Regarding the blurring of lines, where you do homeschool with other parents: there are some minor advantages over public school, in that you would have more control over (1) the teachers, and (2) the class sizes.
My high school (private) was really small. Having the two things mentioned above (teachers who were passionate about what they taught, and lots of one-on-one time with them) was really awesome for me. I got along really well with my computer and math teachers, and I ended up doing some side projects with their guidance (not for credit, just for learning/fun). The experience probably put me a year or two ahead of my classmates once I got to college.
You can get that experience with homeschooling or without. But either way, the parents need to be involved.