I think the issue of dodgy schools is a complete red herring. These schools are known. A school is not an easy thing to hide for long. The government doesn't have the stomach to take the schools on. Given that that is the case, following individual children around is not going to help. It's an ineffective, intrusive and vastly expensive non-solution.
Illegal schools can be shut down. Unregistered, but legal, schools cannot. Some schools take advantage of a loophole in the law which means that they are not classed as schools because they don't offer a full curriculum. The solution to that is to change the law so they WILL be classed as schools and be subject to inspection and control. Neither the legal nor the illegal schools are anything to do with home education.
This argument is a bit like saying we could crack down on unregistered childminders by tracking every preschool-aged child in the country, including those who are looked after by their own parents. It isn't the children, the potential victims, who need to be monitored!