In college, I knew someone who went on to become a quartermaster for the US Army. They were in charge of a group that packed parachutes. As CO he was required to periodically jump with one of the parachutes that his team had packed. Having skin in the game provides a natural incentive to keep quality up.
A commercial airplane is a tremendously complex piece of equipment. Failure can come over time and in unexpected places. But Boeing executives and high level managers should fly commercially rather than having a fleet of private jets.
It will be interesting to see how this all plays out. At this point, it seems likely that they will be forced to take some extreme measures to counteract the bad publicity.