From personal experience, I would say optimizing for higher IQ at the cost of lower EQ to the extent that homeschooling makes possible is a very poor tradeoff - and it is also an extremely easy one to make.
> The oldest is 15, enjoys poetry, plays basketball competitively, likes to tinker with computers, reads history, does math, etc.
FWIW, that sounds like me at 15 and I regret having been homeschooled.