They've admitted that the Willian yellow card should have been rescinded and a penalty awarded. However, it doesn't really matter that "VAR has solved nothing" in a case like this. It's purpose is not to scrutinise every single subjective decision in minute detail and make marginal calls. It's to avoid absolute stinking and obvious howlers like the Thierry Henry handball that took France to the World Cup.That can only be a good thing. Looking at an additional 4 angles of major incidents won't catch everything and there'll still be debatable decisions, but it's better than 1 ref running flat out with his view possibly obscured. Of course, they could look at more angles and more carefully - but if they do that, then it can't be THAT obvious and will slow the game down far too much.
As for 'it's run by refs, for refs", I'm not sure why that's a bad thing. If you mean it's been introduced to cut out the institutionalised cheating that ex-pros advocate week in, week out as 'he's entitled to go down' then I'd say that's fantastic for the fans and the game in general.
I know what VAR is about as you said yourself it’s not about reviewing every decision. However it’s was meant to be used to identify clear mistakes. Last night booking Willians was a clear mistake, like you have said they admitted that. So it’s ironic that something that was meant to correct clear errors did not do its job. The comment about refs is more about the ref who is viewing the video for the ref on the pitch. Next week the roles could be reversed, so yes it’s more difficult for a ref watching the screens to tell a ref on the pitch, ‘you might have got that call wrong’ it should be run by refs yes, but maybe retired refs who don’t have to ref games on the pitch.