Safety is the primary reason to use an officiating body, followed by correct and accountable officiating.
Given that there seems to be little faith in either from most organisations I think that shows must be judged on a case by case basis.
The model that is most touted is that of the BBBoC. The procedure for licensing helps to ensure that boxers are healthy enough and capable enough to compete. The medical requirements are far more thorough than the MT show doc taking your blood pressure and asking 'do you feel alright?' whilst the St Johns sit ringside with a box of plasters. Also on the night hospitals are informed in advance that an event is taking place and two doctors, one of whom must be an anaesthetist as well as two properly equipped ambulances must be on site.
MT shows are similar to the ever growing unlicensed boxing shows in that there is a huge variety of standards in every way, fighters, safety, production etc.
Money is the reason that people do not run events through an outside body, but even if one body were to somehow rise above others and become the official regulatory body, would it help?
Boxing has the BBBoC but unlicensed boxing has never been more popular. On top of that Maltese and Luxembourg licensed boxers who can't get a license with the BBBoC are boxing on shows sanctioned by the GBA etc.
Why would MT, which is already set in its ways, be any different?