Here's the problem. Let's say you run in a road race, but you have no way of knowing if you are running a 5K, a 10K or a Marathon. How fast do you run?
Now picture yourself being a soccer player with no idea how much overtime you are going to have to play. It's tied 1-1 with 10 minutes left in the second half. Do you take chances running forward, or do you sit back and conserve energy? If you know where the finish line is for a road race, you can run accordingly - and in soccer, you can sell out on some hard sprints late in the game knowing that you will only have to run for 5-10 more minutes.
The game would suffer if you don't give the players an idea for how much time they have left. They'd just sit back and jog around.
There's really no great answer for soccer. In the old days (pre-TV) they just played the game again a few days later, but that's an impossibility for this day and age.