There are a number of advantages for a teenager in taking GCSEs. Firstly, the possession of a clutch of GCSEs demonstrates to a college, sixth form or potential employer that a teenager has some kind of basic education and can probably read, write and carry out the four basic arithmetical operations. Another advantage is that a child cannot help but pick up some useful information about science, history and English literature while studying these subjects. It provides a good training ground for the self discipline which will be needed if the teenager decides to go on to college or university. Of course, it is still possible to get a college place or job without any formal qualifications, but it is often much harder. Many of the better universities regard GCSEs as almost as important as A levels. It is of course also possible to acquire general knowledge without studying for formal qualifications, but learning is a habit which can be nurtured and encouraged by regular practice. Systematic study can provide just such practice. Humans are often lazy and many of us avoid thinking about difficult problems if at all possible. Academic study presents the student with a constant series of problems and tasks which must be tackled, whether he wishes to or not. Even if the student does not retain much afterwards, the very act of carrying out calculations involving calculus, say, stretches the brain in a way that it might not otherwise experience. It is like muscle training; the more it is done, the stronger and more agile the brain grows. These are just a few of the benefits which might accrue to the child taking a variety of GCSEs as a teenager. There are of course many others, but these should serve to give some idea of why the project is worthwhile.
The only disadvantage which is immediately apparent to me is that it means a considerable expenditure of time and effort on the part of both parent and child.