In Archery, the participants have to hit the target to get Highest Points, without competitive strategies or competitive tactics.
This is only true of the first round. In the first round, the archers shoot a set number of arrows (72) and are scored by where they hit the target (0-10). But no one is eliminated after the first round. After the first round, the archers compete one-on-one by shooting to see who can win three sets first. Sets in this context are like rounds within one match. Ties count as half. There might not be defense there, but there is competition.
One issue is that breaking up into sets encourages the archers to try their best in each set. Because it is winning three sets that matters. Someone can lose the first two sets by a lot, tie the third, and win the next three sets by one shot each and win the match. If it was simply the total score that mattered, archers who weren't doing well wouldn't have much reason to try in later shots. The sport would be less competitive.
Another issue is that those who make the rules feel that the stress of competition makes shooting more difficult. Example reference:
Shooting in a specific amount of time can be challenging for archers as they have to battle their nerves and stress from competition. The natural fear of competition can trigger the fight or flight response which makes it more challenging for archers to get a good shot.
Whether or not they are correct is another matter. But that's why they chose the format. Because they feel that it makes it harder.
Looking at the Men's Individual Olympic results, this changed who won. None of the top three after the first (ranking) round advanced to the semi-finals, so they didn't medal. The second and fourth scorers from the first round made it to the quarterfinals, but neither the first nor third did. The eventual winner defeated the second ranked archer in the quarterfinals and had been ranked tenth after the first round.
Under your system, all three of the medalists would have lost. Three different people would have won. So it wouldn't just have been faster. It would have produced different results.
If we switch to look at the Men's Team results, they finished the whole thing in one day.
I don't think that time was a significant limitation for them. If it was, they could have simply added more ranges. As it was, they finished all seven competitions in only eight days (24th to 31st in July; out of seventeen for the Olympics). None of the three team competitions took more than a single day. They had time to support more competitors, at least twice what they actually had. Beyond that, they could have added more ranges. Just putting the men and women on separate ranges would have given them an extra day. Putting different brackets of the men's individual on separate ranges would have allowed them to pick up more.