The solution to all of this seems pretty simple: get better referees.
It would've solved Saturday's problem, multiple times. Better refs would've had a better real-time sense of space and time, and one of them would've been able to tell that Luis Díaz was well behind the Tottenham backline when the ball was passed by Mohamed Salah. The goal would've been a goal from the start, replays would've confirmed it, Liverpool would've gone up 1-0 and we all would've gotten the last week of our lives back.
It would've fixed the second error, too. Even much-improved refs may have still missed the call on the field -- it's really hard for the human brain to conceptualize the exact positions, in space in time, of multiple moving bodies and a ball. But more competent refs would've still ended up at the right decision after the Video Assistant Referee (VAR) check.
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If you haven't heard it by now, the released communication between the on-field referee and all of the VAR-related officials was a modern Vaudeville skit, a "Who's on First '' for the digital era. The communication is so vague, so stilted and so easily misunderstood that it's a wonder this doesn't happen more often. Competent communication would've quickly revealed that. No, we're telling you that a goal was scored.
Competence a level above that, too, would've fixed this. Competence among various decision-making executives would've created a better protocol for communication and offered a way to correct an error like this after the fact, during the game.
Pay all of these people more money, attract more people with the necessary fast-paced spatio-temporal-assessment skills, bring in those who thrive in intense moments that call for clear communication and this whole refereeing crisis goes away.
While this view has been expressed to me by people who work in European soccer, it still doesn't address the core of the issue: offside and VAR may have broken each other.