The main advantage that I see to the proposed "New Jump" is this. In any sporting event, you want the contest to be decided on the field of play, not by an arguable referee's decision.
Compared to all the other decisions that go into scoring a figure skating program, deciding whether a jump was a correct lutz, correct flip, intended lutz left the ice from an inside edge, or intended flip left the ice from an outside edge is minuscule. It's almost never going to be the primary deciding factor.
And all the other decisions by the technical panel and the judges (the referee in figure skating does not make any decisions that factor into scoring -- I think you used that word to mean "technical specialist") are still going to be arguable. If you flatten out the difference between lutz and flip and remove that as a point of discriminating between skaters, then some other arguable decision or combination of many on the part of both panels -- number of revolutions in jumps, levels of elements, whether an element failed to meet the definition of an allowable to fill an available element slot, whether to reward or penalize the quality of an element with both good and bad points with positive or negative GOE or just 0s, how to score the various program component criteria, etc. -- will end up being the deciding factor(s). And anyone who disagrees with the final result will find plenty of individual decisions to argue against.
The best thing is when you don't even notice that the sport has referees and judges. The worst is when a controversial judgment call takes the victory from one athlete and gives it to another.
I defy you to come up with a system for scoring a sport as qualitative and complex as figure skating that does not rely on judgment calls.
Redefining lutz and flip and flawed versions of either as all the same jump and allowing judges to determine whether and how much to reward or penalize the takeoff edge only shifts the responsibility of defining the jump from the technical panel to the judging panel. It doesn't remove reliance on judgment calls.
The way the system is set up now, or under the old system to the extent that judges did factor the takeoffs of these jumps into 0.1-0.3 of the required element marks in short programs or some fraction of 0.1 worth of technical merit in long programs, if there are differences of opinions among the judges, all their opinions will get factored into the results somehow, whereas with the technical panel decision, whatever at least two of the three members decides determines the base value of the element and whether or not there's any alert to the judges to reduce the GOE.
In the case of figure skating, you don't want the gold medal to be determined by which skater was out of favor with the technical caller and gets hit with a slew of questionable e's and <'s.
There are three members of the technical panel. It would be very difficult for a single technical specialist to systematically make multiple questionable calls against an out-of-favor skater without the controller and the assistant TS actually questioning those calls and overruling them if they both disagree with the TS.