It wouldn't take up alot of time??!!! Why do you say that? If reruns could only be requested by the refs, we'd find that they'd be covering their backsides all the time by asking for another look. It happens now in cricket where the batsman is quite clearly run out but the umpires still ask for confirmation. If the ref has to walk to a screen somewhere and look at it do you give him a limited time to make his consideration? How many angles would have to be shown -- all of them? Only 2 extra minutes you reckon. I'd suggest you could put a nought on the end of that for some games. If disputed incidents are instead to be decided by a fifth official somewhere then why should he get incidents like last night, with the Lukaku disallowed header, any more right than the ref? It's a matter of subjective opinion in many cases, certainly where there is body contact. At least now you can take your anger out on someone you can see!
The only circumstances that should be considered for more technology are offsides. Live TV coverage already has the technology where a line across the pitch shows who was the last man. Something like that could be run continuously, in real time, to someone sat somewhere close to the pitch and he could be wired up to relay to the ref whether someone has been stood offside. The ref wouldn't even have to stop play and request it gets looked at; he'd be advised automatically, and very quickly.