MD,
Doctors win 73% of medical malpractice cases that go to trial. Perhaps your information suffers from a reporting bias: the narratives that physician-litigants are willing to tell others about, and that resonate with their peers, are those in which doctors are unjustly persecuted.
Lotteries fail to discourage irrationality because the innumerate players’ warm feelings of imagining winning generally outweigh the pain of losing some money from the ‘disposable income’ fund in their mental accounts. However, if the innumerate are made poorer, catering to them will be less important to product designers even if they remain equally incompetent.
The flip side of this is that a more competitive economy with lower barriers to entry and higher returns to ability will increase the relative wealth of the rational, which can improve the world dramatically if they allocate some of their increased wealth to the task. Insofar as a winner-take-all economy produces large concentrations of wealth in the hands of people like Bill Gates, Warren Buffett, and Peter Thiel, it is a fantastic thing.