I think that it's the flow of the game that we fans value the most (apart from our team winning of course!), and also what sets the beautiful game apart from the other sports that have used video assistance, all of which are much more stop/start. In those sports the action also tends to be more condensed or focussed in a smaller area, so making them more suitable for this type of monitoring.
It seems clear that at present the football authorities either don't share our appreciation of the flow of the game, or simply haven't recognised how important it is to the essence of football - or both.