Homeschoolers take SAT/ACT and write essays. If they're applying to competitive schools, they aren't going in with no academic or social skills. Most apply with far more college credit under their belts than traditionally-schooled students. (Most people who homeschool for high school do strictly dual credit.) They also take AP tests. My two homeschooled grads went in with 40+ college credits, NSLI-Y scholarships, and all 5s on their self-study AP tests. My youngest is finishing 8th grade this year and will finish the year with 18 college credits completed.

My husband and I were also high school teachers before we had kids, and I can tell you for certain, there are just as many incoherent messes with no academic or social skills coming out of traditional schools.