This topic has been discussed before on here Harry but I couldn't find the same study this time, but the link below gives the same idea.
The concern with actually stopping the clock every time there's a stoppage, or the ball goes out of play is that genuinely, you could be doubling the game time, if not more. The stats in the worst case scenario in this link suggests that from 90 mins of football, only 47 mins 40 seconds was played - that's basically 50%.
Even on the proviso of going down to two 30 minute halves, theoretically, you could have the 30 minutes injury time (50%), then you could still end up with another 15 minutes injury time and then another 7.5 mins from that 15 minutes and so on. I know that's the extreme, but that initial game time with the ball in play is from a real game, so this would be possible and from just my rough calculations, we'd end up with a game that would be 120 minutes-plus (then add in half time). Some studies suggest some 90 minute game only have around 30-35 minutes with the ball in play.
Then imagine it's a cup game that goes to extra time and penalties, played midweek and we'd all be leaving the ground around midnight!