I think there's two sides to the issue here.
First I think it's a great way for special needs people, people who live far away and have difficulties reaching the school or have any special problems that would have them benefit more from an online curriculum. For the rest of the children, I believe the regular school system would work just fine. The basis I took for this are online colleges, they just don't have the same quality of education as regular colleges which can devote more educational resources to the student other than online material and books that the online courses could provide.
If such an online system is implemented, one way to fix the problem of a parent taking the test for the student is either having the student go to another location, like a school, and have him take a supervised test there. Another solution would require high speed internet access and it's based upon live video stream. You could have a single person supervise a number of students take a test via feed.
A problem I see is hampering social development with the child at such a critical age. It's the age in which he learns how to interact with people and the world and if he's closed up at his home all the time it would just make it real hard for him once he graduates high school. You could make him to extra curricular activity like sports, but not all parents are willing to do this. How many of your school friends didn't do any type of work? At least at my high school, I'd say that about half of them didn't really do anything special outside of school except go out with friends acquired via school. Also you won't have laboratory equipment or specialized classes for the student, they'd just be taking all your basic classes and that's about it. If the student really likes something, like programming, he'd either have to learn it by himself or wait until college.
You do have a lot of distraction at schools, but I think the problem is more with the students themselves and not the system. Parents also get a lot of the blame. The system has been the same for decades, children have the same learning capacity and they learn the same way. Teaching methods have gotten even better but you see more and more problems at school, so what's the problem? It's a number of issues but I think that they can be summarized into two blocks.
1) Students think they can't be punished.
I remember back in pre-school (1991-1993) that if I did something bad the teachers could punish me and that it would hurt. In nap time they'd place me outside the classroom where it was hot (Puerto Rico averages 90 degrees all year long). They could hit you with a ruler, stay inside the classroom for lunch and recess for a week and various other punishments. I knew that if I broke a rule, I'd be in for it quite badly, so my trouble making days were over by kindergarten and I just behaved and focused a bit more on learning. Now if a teacher does what my teachers did to me they'd get sued, lose their license and jobs. Now they can't really discipline their students so you've got students who do whatever they want. This bad behavior doesn't let the students focus on learning, especially in the elementary levels.
2) Students think they have better things to do.
We've all seen it, people texting during the middle of class. They put more attention to their iPod that heir notebook. There's so many distractions that the time focused of learning is reduced. Some even have the attitude that the dumber you seem, the cooler you are, which is a destructive attitude within itself.
Some ways to fix it are just building more schools. The less crowded the school is, the less people the student has to worry about and the less distractions there are. Also give teachers more authority to see as fit. Disciplining a student by beating him is wrong, but there is nothing wrong with hitting with a ruler (up to about 4th grade) or any other kind of punishment. We need to discipline them and today there's not very much a teacher can do. Psychologically, the student will connect the action with the punishment and will cease to do the action if he does not like the punishment. Punishment has to be immediate and something the student does not like. Not this "don't do it again" or "you have detention a few days from now" doesn't work most of the time.
Online school and regular school both have their advantages and disadvantages and should be decided upon an individual basis per student.
None.