To drag this nonsense up again, I hit the giym this morning for the first time in about 2-3 weeks. I did cardio for about 42 minutes. I split my cardio into 7 minute segments. Anyway, I always try to ignore looking at my timer until it beeps, but occasionally I'll look and will be surprised that more time hasn't elapsed. Even if I'm not particularly tired, sometimes I'll wonder if I didn't actually hit the start button. That's the nature of human perception. We always assume we've worked longer hours, exerted more energy, eaten healthier, spent less, etc. if we're not accurately keeping track. So, on top of keeping track of your progress, counting sets and reps is just a much more efficient way of making sure you actually do the amount of work you intended to do.
If you were to hire someone, and you gave them the options of either A)staying until they completed a set amount of work B)staying until a certain amount of time had elapsed or C)staying until they felt they felt like leaving, most people would probably agree that C would result in the smallest amount of productivity.