I think the Spurs penalty is a perfect example of where the referee looking at it themselves again in discussion with VAR (preferably fans being privy to the conversation also) would benefit.
VAR: "There was contact between defender and attacker"
Ref: (Whilst viewing footage) "I saw the contact, I felt it was initiated by the attacker leaning in to the defenders challenge so didn't warrant a foul, and still do"
VAR: "Ok stick with on field decision"
OR
VAR: "There was contact between defender and attacker"
Ref: (Whilst viewing footage) "I didn't see that previously, I only saw contact defender made with the ball. Having seen it again I'm going to reverse my decision and award a penalty"
As it is, the bloke in the booth has changed the decision, where as in the scenario above the ref may have seen the incident clearly and in his mind wasn't a foul, so not a 'clear and obvious' error. Incidents are being re-reffed by someone else.
I just think if the VAR is going to look at the footage several times the Ref may as well look at it too, rather than everyone standing around waiting.