Re "letting Boeing self-certify"
Self certification is not a problem in itself and most certainly not a root cause in this tragic case.
Self certification takes place all around us, most often in very complex areas (my first real job was in self certification of safety examination programmes in nuclear power plants). It can be very broadly compared to accounting and tax declaration paperwork: rules and guidelines are set by authorities (including requirement of, say, external audit), you do the heavy lifting and submit the result back to your respective authority for review. In place of certification are usually strong incentives to do your self certification right. My gut feeling is that in the field of nuclear power generation the failures of self certification which could be ascribed to failing of the incentives were similar in rate to failures of the certification authorities where self certification was not permitted or desired. I imagine the situation may be similar in the airliner business.
It is important to remember that certification in highly sensitive areas (security wise, like airliner building or nuclear power generation) can be either done directly by authorities (who tend to be badly equipped both in personnel and in budget as they run off taxpayer money which over time finds more and more of "better use" elsewhere) or by third parties (where again the situation can be broadly compared to tax & accounting and the landscape of formerly big eight, now big four accounting companies whose history in cases like Enron failure passes as a good illustration). Neither looks like a much better alternative to self certification.