When you eat more than your energy consumption rate, you're less hungry. When you eat less, you're more hungry. You think the activity would stop you getting obese, but it's actually that you aren't hungry enough to overeat, despite high activity.
I'm not overweight, never mind obese. I pay no attention to diet or exercise. If I'm really hungry one day, I can end up overeating something I quickly deep fried from the freezer. And then I barely eat the next day. Not consciously. I'm just not hungry for a long time after I overeat.
Energy homeostasis is the big thing you're not accounting for. Excercise doesn't really do anything much for your weight, just your fitness.
Looking at it from the other angle: can obese people be active and have a balanced diet ?
The answer is yes. In particular you can be obese and maintain your BMI at the same level while being fairly active and not overeating, that happens a lot with people gaining weight and reacting to it, but without going down.
From the pool of people physically active and with a balanced diet, what's the split of obesity is a question I don't have the answer to, but the lifestyle part doesn't look like a good differenciator to me if we're solely focusing on current obesity.
PS:if you eat a LOT more without gaining much weight, imagine eating a LOT less and see very little change.
Note that "have a balanced diet" is doing a lot of work here. Our modern environment is saturated with super calorically dense, hyper palatable food. THAT is the cause of the obesity epidemic -- it's not endocrine disruptors or seed oils or office jobs or anything else.
And the ability to refrain from eating cheap processed food, which has been specifically engineered to hack your brain, requires education, discipline, and willpower. As does hitting the gym.
It's not surprising that most people don't innately have this ability, and have ended up sick from it. That sickness is a medical issue regardless of how we got there.
Had the right approach better results?
If not, why is it the right approach?