I was homeschooled from 5th grade on. The reasons people have for homeschooling their kids varies widely, from hyper-religious to anti-establishmentism to the-schools-here-suck. The types of kids people have also vary widely. So my experience is not necessarily reflective of what your kids' experience might be. That said, here's my story: My options were home schooling or a Christian school affiliated with my parents…
The CAT exams were the same for me, always scored really high and above my grade level. I aced the 12th grade one by age 14. My parents took that as evidence that I was doing well, and I didn't trust them enough to confide just how desperately lonely I was. The CAT (and SAT) ended up being incredibly poor indicators of preparation for college level courses, many of which I failed my first semester despite also being a self-starter who reads voraciously. It was just too much of a jump for me from the unstructured way I'd been teaching myself previously, and I was missing too much background knowledge.
Even with my high SAT scores it was really hard to get into college. I ended up at a tiny private religious school (I'm not religious) because they were the only one that accepted me, and one of the few I was even able to complete the application for because many admissions offices didn't make allowances for homeschooling in their application process (this was around 2001). After a few years there I managed to bring my GPA up high enough to transfer to a state school.
In retrospect, I believe things could have been really different if I'd had access to a councilor with academic experience to explain how the system worked and tell me what paperwork I would need for college applications or what subjects would be necessary for the program I wanted to do. Even in 2001 with internet access I just wasn't able to navigate that on my own and ended up making a lot of costly (time, money, embarrassment) mistakes. And I was a pretty smart kid, I taught myself to code for one. It turns out being smart didn't make up for that much of a knowledge gap.