The MAX fiasco wasn't a case of the FAA being behind the technology, or a case of "self regulation" in the sense of Boeing being left completely alone.
It was a case of the relationship between the regulator and OEM becoming a bit too intimate and comfortable, resulting in the FAA accepting a flawed risk/failure effects analysis to justify a system architecture that might not normally get past them. In this particular case the single AOA vane input channel for the MCAS system, justified because the event risk case was piggybacked onto an existing failure mode (stab trim runaway).
In other words, the FAA accepted Boeing's analysis that the existing failure procedures for stab trim runway (only a "major" event classification event IIRC, in the minor/major/hazardous/catastrophic risk assessment structure), and the associated risk category, made the single channel input acceptable from a risk perspective. In the spinning galaxy of technical and political issues revolving around the whole MCAS story, that's the basic root issue when you dig all the way down.
These sorts of problems that come up during certification, and clever bandaid solutions implemented to deal with them, are nothing new. When you see strakes and VGs and vortilons on wings and tails, they are usually band aids to fix a problem that came up unexpectedly during flight testing and avoided a major redesign. MCAS was a bandaid solution using software and some hardware integrated into the stab trim and stall protection system.
Boeing had a wing flutter problem during the 747-8 certification, where unanticipated aerolastic wing flex problems resulted in a low frequency vibration of the entire wing, fixed by the most amazing band-aid I've ever heard of, using the normally dormant fly-by-wire ailerons as active flutter dampers in cruise, almost entirely with software. You can bet there were a lot of reports provided to the FAA to get that certified.
In the case of MCAS, there was a fairly unique set of circumstances, and a system architecture was approved that shouldn't have been, basically because of too much trust, and key individuals dropping the ball.
And this is the conundrum. The regulating agency will grant a certain amount of trust in the OEM, because the staff level would have to triple if the regulator is going to review and challenge every detail of an OEM's design proposal.
Typically senior engineers within the OEM are granted a delegated approval status by the regulator for smaller mods, and they also become the primary engineering interface with the regulator for approval of the major stuff (in Canada they are called Design Approval Delegates, or DADs). Normally there's a reasonable balance struck when all parties are operating in good faith. This was a case where that failed, but it does work reasonably well 99.9% of the time.