I think it depends on the individual somewhat, and if you are one that has a tendency to be obese, or overeat in general, or just can't give up the simple carbs, then counting calories helps. But I think that if one is eating truly clean (as in a plant-based diet focusing on veggies and avoiding grains, like Dr. Fuhrman's diet recommendations), then it's not necessary to count calories.
I can't imagine that anyone counted calories previous to the last 80 years or so. Or that Okinawans or other fit and healthy populations around the world count calories.
Unfortunately, there are so many high-calorie foods, and 'pseudo-clean' foods, available in the Western world today, that it's hard to avoid the temptation. I think calorie counting comes into play especially when seeking to include these types of foods in the diet.
This question was asked on this forum before, and there are quite a few here, including myself, who don't count calories. Personally, if I find myself gaining weight (because I'm indulging in too many 'treats') I can get back on track just from my dietary choices, not by counting how many calories are in them.