The original post asserted that oprivate schools use unqualified teachers and asked if they are "any good". Subsequent elaboration seemed to suggest that by ubqualified the Op meant did not have QTS.
On the face of it, since most independent schools do quite well in most measures of excellence it has to be acknowledged that the teachers must be doing a reasonable job, whatever their qualifications or lack of.
However , its a falacy to suggest that private schools do have large numbers of "unqualified teachers" Most of those without QTS became teachers over 20 years ago - before QTS existed. Most are experienced and nearly all have some sort of teacher training and even certificates. whether recognised or otherwise (ie QTS). Most younger teachers in private schools will be qualified with QTS or have some equally recognised teaching qualification.
The definition of "qualified" is also traditionally different in a private school. In such schools nearly all teachers would be graduate and by definition are "qualified" (because that was the way it was going back over a 100 years). Private schools still have assistnat masters and mistresses, who can be either graduates or Certificate of Education ( and no degree) . Still though they will be experienced as a large investment is usually made in staff recruitment and salaries to attract those who have some track record of being able to teach, regardless.
Similarly, nearly all teachers in private schools will be teaching their own degree subjects - certainly in senior school. Preps work differently to primary schools too. Very rarely do you get inexperienced teachers in private schools (whatever their formal qualifications).
All that may very well account for their "success" with such "unqualified" teachers.
In state schools,including acadamies and free schools, the situation is clearly very different. It seems as if the freedom to use unqualified staff has been interpreted quite differently to mean effectively inexperienced, maybe quite young and having no teaching qualifications at all. The emphasis seems to be on cheapness. So, you get NQT's and trainees who are still learning or you get persons appointed with no classroom experience at all. Thats quitedifferent to those employed in private schools. You cannot compare them.
Of course , all teachers have to start somewhere. Even I had my first day and my first lesson in front of a group of students. As it happens mine was teaching A levels to adults and teaching undergraduates. For that5 I actually received ten weeks training out of the classroom before I saw a student. My training (which was certificated) emphasised elements of learning theory.It emphasised teaching methods and it taught me the very practical things like how to write a lesson plan, how to break down my syllabus into parts which I could teach in the time slots give etc. After I started teaching, I continued with my course
(which led to a teaching certificate) and went into more theoretical depth of theories, develepment and teaching and management skills.
It took two years to train me. I was teaching all that time and went to my training course for three hours twice a week ( it was Tuesday and Thursday evenings). I wrote numerous essays and read many books.
I was not inexperienced when I went into a school classroom ( ie a secondary school) for the first time. Far from it.