Problems:
1) It would mean much more delay and disruption as we currently don't average anything near two or three full reviews per team every game, let alone even more if the challenge is kept if succesful. So you'd inarguably be slowing things down more and making the game more disjointed, which people would no doubt complain about given they already dislike delays.
2) You're by design introducing greater variance into the decision making process, which will inevitably also lead to greater variance in outcomes. Which means more inconsistency and what fans will call "unfairness". Also if you put a time limit on decisions to address issues 1, that variance massively increases. Assigning blame to the management staff for what they do/don't decide to challenge won't magic away the frustration at increased inconsistency in the way the rules of the game are applied.
3) In your 91st minute example, the manager would already have achieved what he intended which is disrupting the game. Subs only take a few seconds and are also supposed result in more time added on, yet managers still see the benefit in using them in that way. It would be no different for VAR. Games ending in a mess of substitutions and var challenges wouldn't be uncommon and wouldn't be shrugged off by the people who complain about VAR already.
4) In a situation where it's a narrow score going into the final few minutes and both teams have all or nearly all their reviews, that 10 minutes will end up taking forever as both teams start desperately trying to snatch a key foul or penalty.
5) Everything is already reviewed as is. Which means all the decisions would remain as they are now, with all the same complaints following them. You wouldn't have addressed any of those issues, you would just have made them more impactful by tying the loss of a challenge to them. Taking the City offside or Fred penalty shout as an example, both ourselves and Burnley could have reasonably challenged those decisions in the belief they would be overturned based on similar outcomes in different games. In the Fred call in particular, they could point to almost identical fouls where a penalty was awarded. Yet the penalty still wouldn't be given here (because subjective calls will always be subjective and vary depending on the person making them) and now we'd be punished with the loss of a challenge on a decision we know a different ref will have awarded our way. Imagine the anger and accusations of bias. Ditto with handball calls, marginal offsides or anything else. All those problems stay the same.
Fair points all in all. I agree that there's lots of potential problems with general shithousery around challenges as the game is nearing its end. I disagree with the 'variance' bit though as the calls on the pitch will have all been made by the same referee according to the standard he wants to set for the game. If he doesn't give the Fred foul, then he doesn't deem that a foul in the context of this game and can reasonably not be expected to give a foul the other way for a similar incident, which is fair enough for the ref to do.
One of the big problems with this current system is that a dangerous free kick won by a dive, or a wrongly awarded 90th minute corner can be as significant as any other incident on the pitch and there's absolutely no legislation to deal with that. I mean, just a few weeks ago we conceded a goal from a corner that was wrongly given. Now I suppose that can be accepted as part of parcel of the game, and that's fair enough and I could live with that, but the challenge system would eliminate such grievances.
The other big problem that VAR has is that yes, everything is reviewed (or at least we're led to believe that everything happening inside the penalty box is, and everything that might constitute a red card, and if something might constitute a red card then everything that happened before that is also up for review), but they're not reviewing with a view to enforcing the laws of the game, ie "which is the correct decision here". Instead, they're judging whether the call on the pitch was 'slightly wrong', 'plain wrong', 'clearly wrong' or 'clearly and obviously wrong'. That is what makes a majority of the subjective calls take so much time and what causes the "full reviews" that you mention. Most checks would be fairly straightforward.
I remember when Nketiah was sent off for Arsenal for a stamp on a Leicester player I believe. The VAR spent two minutes dicking around with fifteen angles in order to ascertain whether the yellow card was 'clearly and obviously' wrong. After those two minutes he sent the referee to the monitor who went over, looked for five seconds and sent him off. Had he been sent to the monitor right away, the call would've been made in a fraction of the time that it did with VAR first having to decide
how wrong the decision to give a yellow was.
If you take away the artificially created threshold that says a mistake has to be 'clear and obvious', and instead put the main ref in front of a monitor, then he only has to decide whether it's 51% correct to overturn, and that makes for a much better application of the laws of the game and it makes it fairer for both teams as there's not an anonymous guy in a bus deciding what's clear and obvious. So, in my view, the only way to remove the 'clear and obvious' criterion is to make it so that the VAR operator isn't another referee from the same pool of referees who might want to support his friend, as they all tend to do, and instead have the main ref be responsible for the level he wants to set for the game that he's officiating. I understand that referees are different and apply different standards between games, but at least you'd get fairness in the context of the game being played right now.
Now, is a challenge system the best solution? Not sure. Is the system we have today the best one? Definitely not.
The Tyrone Mings elbow on Paul Pogba is something that sticks out with me as to the faultiness of the current system. We have a guy, nowhere near the ball, flying in and elbowing another player in the head in the penalty box, and it somehow ends up not being a penalty. Now, what could the possible scenarios be that lead to that conclusion?
1) It's allowed to fly into players with your elbow while attempting to get the ball but getting nowhere near it
2) It wasn't reviewed at all as a potential penalty or a red card incident
3) It's not allowed to fly into players with your elbow, it was reviewed, but the VAR who's under no pressure from players, managers or fans from his little tour bus hideaway just didn't fancy alerting the referee to it because he loves Graeme Souness and hates Paul Pogba
4) It is not a clear and obvious error to not give a foul for a flying elbow
As for 1), that's clearly not the case. As for 2), we're led to believe that everything is checked even if the graphics don't show up, so you'd reasonably believe that the VAR spent the two minute break reviewing the incident while Pogba was filmed, bleeding from his mouth. That leads to the conclusion that it's either 3 or 4 that is the case here, and the threshold to overturn a non-decision will have played into his mind. Also, it's much easier to play into pre-existing biases when there's nobody next to you demanding that you make the right decision. Had the ref been put in front of the monitor himself, he would've had to think that "I'm going to look stupid if I watch this and don't give a penalty as it's a clear violation", which would take away possible bias and instead make him focus on what the correct decision should be.
