This question is decades old and comes up from time to time, usually when a tragedy like this happens.
I should start with a disclaimer. The probability of being involved in, let alone injured or killed by, an airplane crash is small. The probability of this happening to people on the ground not involved in aviation is even smaller; it is astronomically remote. If you consider the benefits aviation provides: lives saved in medical airlifts, disaster evacuations, providing fast, safe transportation of goods and people, the overall cost-benefit of aviation in general is overwhelmingly positive. For every person injured or killed there are hundreds if not thousands of lives saved or improved. That doesn't do anything for the children tragically killed in the above crash, but it should guide our reaction to it and inform public policy.
There is some truth to the notion that general aviation kills doctors and similar financially successful people. Successful people are usually intelligent, competent and hard working. They are very good in their area of expertise and usually are fast learners who are good at many things. But that doesn't mean they're good pilots. They overestimate their piloting abilities and their wealth enables them to fly bigger, faster, complex airplanes that are less forgiving. A little mistake that might not even be noticed in a C172 can kill you in a TBM850. This has a thread of truth but I believe it misses the real point.
Rich/successful people may be over confident but that's not what really kills them in GA. What kills them is lack of clarity around what constitutes "piloting ability". The conscientious wealthy pilot seeks out training commensurate to the airplanes he flies. He develops all the skills and knowledge that are available from the best trainers. He departs into the sky with confidence. But it is a false confidence if he doesn't realize that piloting is more than skills and knowledge.
Skills and knowledge are essential, but judgment and discipline are even more important. Poor judgment can get you into situations from which no amount of skill can save you. Have a look at some of the most common causes of aircraft accidents:
They have little to do with skills or knowledge. They have a lot to do with poor judgment and lack of discipline.
My personal opinion is that judgment and discipline cannot be taught.
Some people have them naturally, others build them from experience, and some never develop them.
If a pilot upgrades his airplane too quickly,
before building sufficient experience,
he may lack the most important aspect of piloting that no amount of training can ever teach him.
Any extra training he has will certainly help,
but he always more likely to be killed by lapses in judgment or discipline that:
It may be that wealthy people are over-confident.
If they are, it contributes to the problem, but it's not the root cause.
The root cause is a chain: