According to recent reports, when maths A level papers are re-marked, only 4% end up with a changed grade. The assessment is bad, in my view, but at least in a consistent way which, because it is algorithmic, is open to discussion and review.
In subjects like English Literature, Drama, Art or History, the figure is 40-odd per cent. I'd say the answer is just not to have school exams (or, probably, university exams) in those subjects.
"Diagnostic testing" in schools is useful. That can be reported to the student as the teacher's judgement, subject to being queried by the student and with the option of being checked by another teacher's. It doesn't have to be a grade. (When I was teaching in Queensland, Australia, we were, for a while anyway, banned from giving our assessments false "objectivity" with a numerical grade, even in maths).
"Summative testing" is important to check whether people are qualified to do jobs, as doctors or electricians or bus drivers or such. It should be as algorithmic as possible, pass/ fail, and open for trying again if you have a bad day.
No good purpose is served by exams in schools. At the best (and most of them are far from the best) they test ability to do... the sort of exams that are set, which have very little correlation with anything in "real life".
To decide which of two novels to read (or deciding as a publisher which of two scripts to publish, or deciding as organiser of a poetry reading which of two versifiers to invite), would you go by a report that author X had got an A in an Eng Lit exam, and author Y only a B? You would not, and you should not.