If more than half the overturned decisions are correct, there is an increase in the overall amount of correct decisions in the game. I would suggest it is significantly more than half - because if it was anywhere near wrong half the time, then there would be a DRS error every second match - there quite clearly isn't.
Actually your argument for DRS is very stats based. You keep saying that if more than half are correct, then we are still getting more correct decisions. I am saying stats don't matter, and if poor implementation of DRS, leads to the very error it is meant to protect against, even in one case, let alone the several well documented cases, then as a concept the system has still failed.
I'd suggest the solution to that would be to specifically train umpires that are specialist third umpires, not occasionally put field umpires up there for a stint. Professionals specifically qualified to operate the DRS, which is a different skill than being a field umpire.
I would also give them the ability to not make a judgement and return the decision to the field umpire - the third umpire previously had that ability on close run-out calls, they would have a white light in addition to the green and red ones to signal that there was too much doubt. The fact that the umpire can't just say that it is inconclusive, uphold the original decision and return the review to the team who asked for it, is a problem. The umpire currently has the pressure to make a decision, indeed to overturn decisions in close calls, because they would impact the game regardless by the team losing a review.
As for all the potential corrective steps that you write, and indeed the many corrective steps suggested by me in the past, if they help I am all for them being implemented. However the point is you dont finish a product by a trial and error method at the top level. First it should be tried in the lower levels and then brought to the highest level. Imagine a situation, where in a WC, a guy misses out on a fighting 100 because the Umpires don't know something as fundamental as once they have given a batsman out and DRS is invoked, the ball is dead.
You cannot then run out the non-striker as an insurance.
That just shows how ridiculously casual the ICC is about fixing DRS issues, and it frankly drives me mad. How can you not bother to teach the Umpires rules even the very basic rule to invoking DRS. Lets not even go into the actual DRS misinterpretation of Akmal.
So let's use the example of water - if running water through your hands removes 90% of dirt and the filter gets that up to 95% - the filter is worth it despite the fact that occasionally things might fall through that your hands might have caught. If it removes one more toxin than not using it, you have made a net improvement in water quality. That's a good thing.
Again you have missed the point about the Filter in the example. Its okay that the Filter cannot remove the remaining 5% of the dirt despite its best efforts, just as it would be okay if DRS couldn't really do anything about the 2-5% umpiring errors that still happen. However if the Filter itself started to leak toxins into the water, the very toxins it was meant to remove, even if in very rare cases, would it be okay then?
Even if say the company produced a million filters and in only 1% of the cases, the filter instead of removing the toxin from the water, was found to actually add more toxin to the water. Would the company then not have to recall the product.
Similarly the DRS is not an innocent filter that cannot do anything about the toxins (errors) that still seep through. Inconsistency with DRS tech and interpretation is actually leading to errors (like the Akmal one, a Batsman n.o., was given out as there is no consistency in how an umpire will interpret DRS). DRS and its interpretation has to be uniform and consistant, and there just cannot be a situation where two umpires can look at the same replay in DRS and arrive at two different conclusions.
Thus as with the Akmal decision, DRS is actually adding the very toxins (errors) to the water, that it was meant to remove. Even if this is in very rare cases, the very idea of having a filter is violated, and it needs to be recalled. Or atleast needs a very very hard look at.