In terms of how VAR is presented to fans, having the decision on subjective calls made by the referee looking at the monitor on the side of the pitch would be a lot more palatable, I think.
Even if you disagree with his subjective decision, it would be clear to absolutely everyone (at home and in the stadium) that the decision was looked at and that the referee took responsibility and made the call himself having seen the incident in its entirety (the contact, the context, the exaggerated reaction of the fouled player, etc.). Rather than two different people looking at subjective decision, you have the person who has always been making the subjective calls making the best subjective calls possible with the aid of VT. If you don't agree with the decision you know exactly who the responsibility lies with, you know VAR did its job in giving the ref the opportunity to make the best possible call and you know the call he made was (in his opinion) just that. It's all on the referee (just as before) but the referee will be making better calls.
Whereas as is we see the ref and players mill about while a discussion we can't hear takes place, which results in a decision. Even if this process gets as many calls right as the above there is still less confidence in the process due to the uncertainty as to where the responsibility lies, what informed the ref's original decision, whether there are conflicting views on the subjective decision from VAR, etc. Much less clear and (despite probably being quicker) much more frustrating imo.