Not even Liverpool's worst detractors will chalk their record up solely to lucky VAR calls. Klopp has spent a handful of (well-resourced) years building this squad and we are now seeing the fruits of that. Klopp is not perfect, but in terms of transfers, tactics, player management and personal deportment he's gotten it right much more often than not, and he's also been supported by the club.
(Warning - VAR-related ranting)
Sheffield United just had a goal chalked off for a very marginal offside, and City went on to score and are thus currently winning 1-0. Should be 1-1, according to the VAR conspiracy theorists...but if that's true, the VAR-haters are effectively arguing that the offside rule is wrong...maybe an attacking players should be allowed to be a little bit offside, they say...because the "offside by an armpit" calls just aren't common sense. The game's gone!
The problem here is that VAR is great at measuring things that the naked eye cannot see in real time, and I honestly can't think of a fair alternative to the rule as written. If we relax it, how much? An inch? a foot? How do we consistently measure that? Will that be fairer from the fans' perspective?
VAR solves some problems and creates new ones. Welcome to real life. VAR is successful as a technology, but it does fail on one key count - it does NOT reduce the number controversial refereeing decisions, it simply adds a new factor for people to complain about.
Society, inside and outside football, is still (wrongly) convinced that we can employ technology to solve social issues. People complain about calls as much out of tribal loyalty and passion as from a genuine concern over fairness. No technology will ever end the bellyaching.
In general, I favour VAR, and - as with any form of technology - I imagine that as it becomes more familiar, and teams (and managers and their back-room teams) become accustomed to it and used to it, and learn to plan for it and adapt to it, that conventions, and understandings and guidelines will grow as to how it should be used.
It does seem to have curtailed some of the worst fouls, and that dreadful practice of diving, and it most certainly has advantages.
As you say, it solves some problems and creates new ones.
Adjusting and adapting to the new problems posed by VAR will take a couple of seasons, but I expect that VAR (ranting of old-timers notwithstanding) is here to stay, and how it is used will probably be tweaked in the light of a season's experience of operating with this system.
Notwithstanding all that, it is clear that Liverpool are as good as Manchester City were both last season and the season before, if not better.
People forget how good they were last season, losing by a single point to Manchester City, having lost one game all season, and claiming the Champion's League, when they had been runners-up the previous year.
Their biggest problem is neither nerves nor confidence - winning the Champion's League will have done marvels for their confidence - but the possibility of serious injuries to players in key positions at a stage in the season when that may still have an effect or impact on results.
