The MAA came into existence as a result of lessons learned thanks to Haddon Cave. Any lessons learned would have been of very dubious value as his report falsely described the period in which the Air Safety system was subverted by RAF VSOs as a "Golden Period" and instead named SOs (ie 1* and below) as responsible at a later date for Nimrod airworthiness shortcomings.
As for Safety Systems, Sean Cunningham's had no published Safety Case and it killed him. It had no Safety Case because those engineers within the MOD whose job it was to ensure that it had one were got rid of, and their knowledge went with them. To admit that would reveal the subversion that led up to it and the illegal actions of those VSOs. That is presumably unacceptable, so the cover up continues and the MAA remains compromised together with RAF airworthiness.