It probably does depend what your school situation is.
We are fortunate to be in a very good, well-funded public school, which is rare. The gifted program here starts in 4th grade and is full-time. Through that, my son will do honors Geometry in 8th grade, then do two years of AP calculus in high school (AB, then BC).
He tested into 5th grade math in 1st grade; his reading is 2 grade levels ahead. They feel he could easily handle a grade skip. If we grade-accelerate him for math, sure, he could do college math at the local university in h.s., but I suspect that would be a problem with scheduling his classes.
I was HG and grade-skipped. Academically, it was easy, but socially, being the youngest/shortest in h.s was hard. Going through puberty later, driving later, was hard.
I graduated with honors in a science major from Northwestern and honors from Harvard Medical School. It took me a long time to realize that there is so much more life than simply being the best academically. Having good social skills is very, very important in the work world.
My son is hearing impaired and has some learning disabilities related to that. He wears a hearing aid. He has a very good work ethic, to overcome those, and I suspect he will do very well.
In college, there were a few HG people who had radically grade accelerated. They tended to be extremely freaky and do very poorly in jobs/getting jobs. There were very few like that at Harvard Med- it was just too competitive a school to accept someone who was just 2E and didn't have the whole package.
I think many kids who grade accelerate may miss out on the "whole social package."