what then is your solution to the accidents where apparently incompetent pilots crash perfectly serviceable aircraft
And who said there must be a 'solution'?? Do you have a solution for lapses in human judgement?
What is a solution for a perfectly competent driver who one day decides to run a red light or overtake another car on a windy mountain road with not enough room to spare?
I suggest you read some accident reports from GA when many of them state 'lost control for unknown reason' or 'decided to descend below MDA in poor weather', etc, etc. What institution can be blamed since no airline is involved??? FAA for not flunking a pilot in his verly early career?. How can you predict that a pilot who keeps passing all known competency checks will do something irrational or will be guilty of major abrogation of his duties in say 8333 hr of his career??
I don't have a solution but certainly consider it a gross naïveté to think you can subject pilots to more training or 'better' training and somehow avoid those accidents unless you can unambiguously enumerate deficienices in their training (like in the caseof the Polish Tupolev pilots that crashed their presidential Tu-154).