Burgers produced is the best example. It's simply about the amount of work you get done. I don't think the criteria you'd use to gauge quality of work in those other areas applies to working out. Not to me, not in an obvious way.
I'm only pointing out that none of these things are equal. We think its silly to say we can't count burgers only because "nothing important" hinges on their "minute" differences. We're just as comfortable counting them as we are uncomfortable trying to count (e.g. for commoditization) academic papers, on account of how difficult it is to compare the latter.
If two burgers satisfy us the same, we say they're the same without too much scrutiny. Reps and sets are mostly the same way. But when you wake up thirty years later and decide to go to five guys instead of Burger King, or end up in the ER from a heart attack, you start to revalue all those bland whoppers you ate or low fat veggie burgers you skipped.
I look around and see (not only in the gym but everywhere) lots of people chasing after numbers, seemingly in a circle, all in the name of some abstract "progress" or "optimization" which only seems to exist in their imagination. From my perspective, they're only suffering myopia, with "nose to the grindstone" wearing themselves out. And I suffer this way myself, we all do, inasmuch as we think ourselves rooted in the right spot, ready to systematize and build on our foundation.
The way we obsess over workout schemes just seems a particularly notable example of this short sightedness, since no one ever makes progress for long, yet we carefully count the tiniest portions of each workout as if it's a serious matter.
You know, I am really not dogmatic at all when it comes to fitness. Whenever people who don't workout ask me what they should be doing for arms or chest or whatever, I just say the most important thing is to get on a fitness program and stick with it consistently. If you have found something that works for you, great. The problems you've had counting sets and reps just aren't problems I can relate to. I like gauging my progress accurately week over week. Counting reps enables me to focus on increasing my reps within a single workout. I don't sacrifice other aspects of progress to increase my reps. I like to keep my workouts as close to an hour as possible, so counting reps and sets allows me to get in all that I want to do while staying on that schedule. For me, no problems have arisen from counting. Everything has been advantageous.
That's good man, it seems our perspectives differ because I've been less successful and questioned our counting scheme a little more, consequently.
Back when I was gaining muscle and strength regularly, I didn't question the fundamentals (as much).