People maybe are focusing on words here. It's better approximated by saying
- Control weight with calorie intake and increasing NEAT
- Be healthier with exercise.
There is a grey area where NEAT and Exercise overlap. I would nearly always bucket anything that could be considered NEAT as NEAT.
I'm definitely not.
I'm talking about a big picture approach.
I set my calorie goal at the lowest safe number. I estimate my TDEE using myfitnesspal set on sedentary, and tell it I want to lose 2 lbs per week. I consistently lost about 2lbs per week this way. My target when I started was about 1650, now it's 1500, and it will go down as I lose weight.
If I set myself to moderately active, it would take into account the NEAT you're talking about (non exercise activity). But I don't, because I want to count my running and I don't want to double count it by saying I'm active AND I went for a run.
I try to meet that goal every day. It's difficult for me to restrict myself to 1500 calories, but right now that is my lose 2lbs a week goal. That might seem high to you but I've been doing this for a long time and I am pretty close to exactly 2lbs per week when I follow myfitnesspal so for me it works.
1500 is a realistic BMR for someone sedentary who is not overweight. But right now it loses me 2 lb per week. That is because I'm fat and am not completely sedentary.
If I want to earn more than 1500 by exercising I can. That motivates me to exercise. Work more eat more.
You suggest ignoring those calories. That motivates me to exercise less. At your job would you work more to get paid the same?
You rely on your intrinsic motivation to exercise, and encourage more accurate calorie counting. I rely on the process to reinforce good habits and permanent lifestyle changes, and am willing to trade off some accuracy on my calorie counting. If I lose 1.5 lbs this week instead of 2 but get in 3 good runs, 3 rows, yoga and some pushups/eips/kettlebell swings, I'm better off than if I burned 2 lbs and did a couple workouts out of obligation.
Remember that I'm still making newb gains - which means I can add muscle on a caloric deficit if I have enough protein and rest. You probably can't cut and bulk at the same time.
Also remember that I'm cutting a lot of weight, which means I'm losing a lot of muscle mass. You can't expect to lose large amounts of weight- in my case over 100 lbs - without losing any muscle, but if you eat your protein and work out you can gain back some of the muscles you're losing.
So my approach is wildly different from yours, because my goals are different.