Parents, when money isn't an obstacle, do you choose homeschooling?

My sense is that with unlimited wealth, homeschooling is always the best option since you can hire the world's best tutors to provide 1-1 instruction for your kids in the approach that works best for them - and evolve that as they grow. From an educational standpoint, can any K12 private school compete with a homeschooling education since its 1-1 mastery-based learning?

If we look at how kings have educated their kids in the past, and how a lot of Silicon Valley parents are doing it, it seems they opt for private tutors. And, also every affluent family uses a ton of tutors when they want to give their kids an advantage in school. Most parents would naturally choose an SAT tutor over an SAT group class if they can afford it, because it's evident that will be more personalized - and they can choose the right teacher.

It seems to me that every private school is still doing group instruction (not 1-1 learning), even the best private schools don't offer an amazing salary to the teachers (not even junior engineer level) so that limits the talent they can attract.

On the other hand, maybe elite schools provides more of a chance to connect with other gifted kids (though not sure if that adds more value than a gifted/well-educated adult).

I'm asking this with separate from the debate around socialization which is a highly loaded topic (and there are plenty of active homeschooling communities especially among world schoolers and big cities)