What if how the child wants to learn isn't the best way of actually learning the subject? Of course your AFL strategies can help identify that and provide the right level (and interval) of feedback to help guide them in the right direction...
If you don't want to worry about exam technique, then no problems, but your child will then get less than they are capable of, possibly dropping a grade or two.
If you (or they if you let them) choose to do a subject that has some level of controlled assessment (e.g. All four of the recognised UK computing GCSEs) then surely knowing what the exam board is actually going to mark is somewhat worthwhile?
Unless of course you are going down the route of not having them take the recognised qualifications but that may make life somewhat more difficult for them if they decide that joining Daddy's alternative lifestyle outside of "mainstream" society isn't for them.
One massive positive about home schooling though is it does allow you to isolate your child from dangerous ideas that you disapprove of. Possibly why it is so popular in the US amongst the religious conservatives.
You seem to be mixing up the principle of "How" you learn with the principle of "What" you learn.
Teaching in a style which keeps a particular child interested in learning is, in most cases, going to be a more successful way of teaching than using the accepted "best" teaching delivery method.
Schools are set up to, first and foremost, make sure all children are afforded a bare minimum level of education to take in to adulthood - hence the trend for teaching reading using Phonics despite its detrimental effect on the better reading children. And the measurement of schools being based upon getting as many pupils as possible to attain a C-grade or above.
Children who are outliers, sitting apart from the main group at which teaching is aimed, are particularly poorly served. I've been there - being top of the class with little effort really eats away at your motivation until you get to the stage where the work does actually require some effort (A-levels), but you can no longer put effort in.
Home schooling should, in theory, allow tailored teaching which should be a huge benefit. It needs to be performed correctly, though.
As for the social issue, I agree with the need for children to spend time among their peers, but I think we're kidding ourselves if we fail to recognise the harmful environment schools actually incubate with the sort of bullying and unhealthy peer pressures which impact upon many children. We call it "character building" but, frankly, I'm not convinced it builds character in a good way.