I've been banging this drum since VAR's inception. The "clear and obvious" thing is ridiculous. It comes from an attempt to by referees to protect the idea that a bad decision made in good faith is somehow less wrong and any challenge questions the integrity of the ref.
It's only referees and idiots with no critical thinking skills that parrot the "We don't want to see the game re-refereed" line. Yes we do. We want to see all the available tools being used, as other sports do, to attempt to reach a correct decision, and when "correct" is a matter of opinion, it should attempt to divide that opinion as equally as possible, not make the arbiter of "truth" one man who's seen something once and only from his POV. Nobody ever said they wanted VAR to do that that other than refs who never wanted it the first place.
The other problem it manifests is refs leaning on their VARs to help them make decisions that they don't have a clear view of, eg penalties that VARs then don't feel they have the authority to step in for. That's a proper crack. And the PGMOL making a mockery of the laws and their own guidance on them with their excuses on Monday morning and on that waste of time Mic'd up thing with Michael Owen where they try to gaslight everyone into agreeing that clearly bad decisions are okay if you look at them a certain way.
I don't agree with this. Most fouls in football are subjective. It's not like cricket where the ball either hits in line and would, with 95%+ accuracy, then go on to hit the stumps. You only have to look at the numerous decisions which are debated every weekend to see how subjective football is.
What is a foul to one referee may not be to another, and that's the unfortunate reality of the sport. You can try to standardise as much as you want, but that will always be the case and there will always be grey areas. Therefore, with VAR, you have the following options:
1. Let the on pitch referee have a look at his decision again on TV. They tried this, nobody seemed impressed by it. It took ages, and the ref almost always second guessed himself and decided that he was wrong.
2. Let another ref review the first ref's decision. But why should the subjective opinion of that second ref take precedence over the opinion of the first ref? Then you are simply "re-refereeing" the game from the perspective of a different person's take on the laws.
3. Only allow a decision to be overturned when the error is clear and obvious. I do not like this solution at all, for the reasons that everyone has set out above. But I think it's better than 1 or 2.
4. My preference is to allow the teams playing the sport to challenge a certain number of decisions per match. I'd then suggest that you have a panel of three refs, one of whom is the on field ref, voting on whether the decision was correct or not.
In short, I agree with your criticism of the "re-refereeing" line, in that I agree that we want to use all of the tools to get to the right result. But to my mind, the "right result" is not just the subjective opinion of person 2 overruling that of person 1 - that is the very definition of re-refereering.