We've had really slow decisions on offsides recently anyway, the difference being a goal being disallowed or allowed incorrectly after it which changed the result. Also after poor decisions we usually get players arguing back because some will know it's wrong, which adds to the delay.
When you have a video replay the confidence in said decision will go through the roof with mistakes being incredibly rare, as a result players will after a very short period simply stop fighting said decisions and get straight back on with the game. When you feel aggrieved that the refs/lino has made the wrong call you won't accept it, when you feel like it's 99% likely to be accurate, you might be disappointed but you'll feel it's a fair decision and feel no need to argue with players surrounding the ref.
The delay wasn't at all longer than normal controversial decisions. However if you're into football, you're already dedicating lets say an average of 45min travel time each way, 90 mins of normal time, 7-8 mins of extra time, 15 mins of half time..... but adding 90 seconds of video replays ruins the day? Fact is after all that travel and on average lets call it 110mins start to finish, ultimately fans will feel far better seeing a fair result than wasting that time just for a ref to cheat you out of a fair result.
But another HUGE point that gets overlooked is the time video replays will save. If you have a system where like a lot of other sports, maybe managers get 3 challenges but lose one if they are wrong, then things like dives for penalties, dives to get players sent off, shirt pulling in the box, over a course of a few weeks of loads of challenges in a match, red cards and teams losing games due to diving and shirt pulling, after a few weeks players will stop doing these things entirely. So that 2-3 dives a game where a ref wastes time arguing with players who say they didn't touch the other guy, players pretending to be injured to try to get the other guy a card, dead play while they wait to take a freekick/penalty/be fake treated by a trainer/arguing, that will all pretty much stop and save a hell of a lot of time.
Currently players dive because there is a big payback in terms of risk/reward, players pull shirts for the same thing. If diving means an almost certain yellow card because the other player tells his manage to review the decision then players will stop diving.
I would have no problem if video replays meant major decisions added 90 seconds to a game, or even 4 minutes, I'd prefer to watch a fair game than a marginally shorter unfair one. But the reality is having video replays will stop a LOT of cheating and prevent a lot of stoppages in play from diving and players arguing with refs.