It can be a difficult thing to get your head around, so let's think about it differently:
At the moment, the clock stops when the ref blows the whistle and it restarts when the whistle is blown again.
In reality, the clock doesn't actually stop but a second clock runs during those stoppages which is then totted up at the end of each half to determine "stoppage time".
The issue with this system is that there are many situations during a game where the ball is not in play but the whistle
isn't blown. Goal kicks, corners, throw-ins. These situations are a genuine cause of timewasting because this time lost isn't added on, and according to the LotG, shouldn't be. A "stopclock" would solve this problem because it wouldn't run unless the ball was in play.
The biggest cause of timewasting debates is a player going down and/or receiving treatment. This can only happen if the physio is signalled on by the ref, who must blow the whistle to allow that to happen. Time lost here should absolutely be added on and the ref is responsible for it. A "stopclock" would solve this problem and it should guarantee that no time is lost. There would still be a debate about breaking up the game / momentum but no solution is perfect.
That gives us two problem areas which would be solved by a stopclock.
This is a breakdown of the top 4 English divisions. In the Championship we typically watch only 52 minutes of play and in League Two that figure is just under 50 minutes.
There would be a bit of a transition period, but under the current conditions a 3pm Saturday game in the Championship would finish at 5.06pm in order to get 60 minutes of play. However the game would soon adapt, as there would be no longer be such an incentive to waste time. I'd expect games to quickly start finishing roughly when they do now, around 4.50pm.
I think some people are seeing "60 minutes" and thinking games might finish at 4.15pm, but this misses the point. Some of the stoppages will still happen, the natural ones like fetching the ball back from the stands, but that time will no longer be counted towards playing time. So you'll be watching a game that takes around 90 minutes to complete from kickoff, but you'll be guaranteed 60 minutes of actual play.