alt Hacker NewsAs has been noted in several of the comments, the crashes were a result of a faulty design, not aircraft failing to meet the design.
The self-certification here wasn’t part of the chain of events that led to the crashes; it appears to have been related to other issues the FAA uncovered as a side effect of their investigation.
As has been noted in the actual reports, the crashes (as is true of all crashes) were the result of a specific chain of failures across several functions and organizations.
One component of that chain of failures is the self-certification process. If the FAA had the resource and mandate to actually understand each aircraft design change, then it's very likely (not guaranteed, but very likely) that the MCAS design having a single point of failure on the AoA sensor would have been flagged as problematic by FAA.