Many people like an Econ-101 "free market", with perfect information, competition, and zero barriers to entry for competition or lock-in for customers. This never exists 100% in real life but often it's close enough. Here, not so. For aircraft construction, a specialized field with long lead times and expensive products, the barrier to entry is huge. So competition is thin.
Which is all a good argument for regulation, and why the FAA exists, maybe our aircraft safety standards need some updates.
IMO, this is the system WAI: Boeing pushed the limits, had a high profile incident (in which injuries were minor), and is now reeling to rebuild their reputation with regulators and in the market.
Of course Boeing self-certifies planes. Who else is better equipped or incentivized to not fuck this up?
The bolts in that door plug weren't installed; it was a one-off due to some maintenance work. Do you propose the FAA systemically review every bolt in an airplane before they declare it airworthy? Every third bolt? Every third bolt of every third plane?
At what point do you just accept that fundamentally, nobody other than Boeing has the resources to check that a plane is safe?
The party to blame here is Boeing. The FAAs job is not to make sure they never step out of line, it's to correct them when they _do_ step out of line.
The FAA is doing their job just fine - I'll remind you, again, that even flying on the 737 MAX is quite safe and you still run a higher risk of death on the drive to the airport than on the plane.