I think video evidence should still be used, but the video ref (IMHO the senior ref present, so that experienced refs still have a role when they can't run around on the field) gets only a certain amount of time to make a decision. If he can't see something in say 30 seconds (maybe 15?) then the incident clearly isn't obvious and the decision of the ref on the field stands. I'm only suggesting video evidence for the most obvious stuff that the refs still manage to miss (like today's "pen" at Chelski), whilst if something is not clear cut then it's not surprising that the ref on the field might make a mistake, just accept it.
I really don't think the authorities will ever go for it though, because it's always been the biggest teams that have benefited from the dodgiest decisions. I don't think refs are biased (well some are) but there's all sorts of psychological factors that might result in them favouring certain teams under certain circumstances.
I just want the right decision to be made. Not much to ask for!
I take your points vim and I like a lot of what you say, but at the same time I think that either you do this properly, or not at all. A compromise just gets messy IMO. Putting an arbitrary time limit on decision making leaves just as much scope for error and if you're going to have a time out for a video review then you may as well take 2 minutes or more to get as correct a decision as possible, as take 30s. What if there was one more key angle that might need reviewing for an extra 10s, but they don't get a proper look at it until MOTD?
What is great about some of the integration of technology (goal line tech for example, and my bugbear of miking refs and transmitting the feeds) is that the effects are instantaneous - you instantly get clarity on clear situations, whether that is the ball crossing the line or foul language towards/harassing the referee. I think if you're going to go down the route of stopping the game you have to allow the stoppage to go on until as correct a decision as possible can be made on the pitch. As much as we all want correct decisions 100% of the time where the situation is clear-cut, to me stopping the game indefinitely to get a decision made on-pitch on all situations, whether black and white (however complicated) or situational and nuanced, just isn't how a football match 'feels'.
What could work is a rugby style 'advantage' system, where a ref or linesman (or even a captain or coach, if you wanted to extend the system - refs/linesmen would have unlimited access, and captains/coaches would have a tennis-style 3 referral system) can ask an experienced official 'upstairs' to check a situation in real time while the play continues. Then if it turns out there has been an infringement that can clearly be proven (an offside, a corner vs. goal kick, or contact in the box where it was thought there was none etc.), then the play gets bought back and the time in-between added on. That is a fairly major rule change and would take a lot of getting used to (and isn't foolproof as it still relies on one person's interpretation of potentially nuanced situations) but to me, would be better than having a timeout system where the game fully stops.
To use an example recently that affected us - let's say that Toby raised with Lloris during the EL game that he hadn't conceded the corner that led to their equaliser, that it should actually have been a goal kick (as it should indeed have been). Toby flags to Lloris, who then signals to the ref or Poch that he wants it checked. While its being checked, they score from the corner. Then, the decision having been checked and overturned, the goal is disallowed and we continue play from our goal kick, with the time in-between added on at the end of the half.
I've literally just made the last 2 paragraphs up so the system I'm suggesting would need further refinement, but I prefer it to stopping a game of football like they do in rugby.