The time commitment is actually way less than you would expect. The amount of "fluff" that goes on during the school day is obnoxious. You could probably spend less than 3 hours a day and get a better education.
By the way, school is not the only answer for any of the questions you asked.
I don't think anyone is claiming that the ideal homeschooling childhood consists of only interaction between parents and child, and nobody else. Neighbors, fellow homeschoolers, family, church, Scouts, camp, trips, actual adults: these are all sources of socialization.
[1]I went to public school and it was good. But I'm open-minded to alternative forms of learning.
Consider that an average class consists of 25-30 students; this means that for every hour of class time, your child averages about 2.5-3 minutes of one-on-one instructor time if the teacher did nothing else but work directly with individuals. Obviously in practice this doesn't work out: there are announcements, lectures, assemblies, fire drills, time for individual reading, and of course some students will demand more of the teacher's time than others either due to behavior problems or simply because they vocalize their need for help better than other kids.
Compare this to homeschooling, where the student-to-teacher ratio is much lower, and the teacher is intimately familiar with the student's strengths and weaknesses.
Also consider the teacher's motivation: it isn't a general love for teaching coupled with sticks & carrots imposed by the school, district and state but rather a parental desire for their children to learn and succeed.