I had a somewhat similar question about exercise vs physically demanding work, since the former helps to have a healthy heart and the latter seems to do the opposite. Explanations I've found were tied to the average daily heart rate. Exercises are intense but it's only a few hours per week, and over time they tend to lower the average heart rate. Physical work is typically less straining but it takes a big portion of the week and as the result increases the average heart rate.

I guess the problem of exercise (intense but short) vs chronic stress (moderate but 24x7) could have a similar explanation.

I don’t think the claim is that it just uses energy, it’s that it uses energy to the detriment of other processes.

The body is extraordinarily complex, so I don’t think you can extrapolate that to anything else that uses energy.

Any garden variety gym rat will tell you that when you worked out you eat a lot more. And that may be the same for stress, but perhaps what your body does with the energy when you exercise is different.

The body tends to use the same amount of energy regardless of what you do in a day. You can certainly over exercise which causes undue stress on the body. However other than an adaptive period at the start of regular exercise your body adapts to the increased caloric use from exercise by down regulating other processes to conserve energy. Typically an excess of calories is used by production of lipid fluid in adipose tissue and over expression of global inflammation. Once you begin exercising regularly the body generally stops using stored lipids for extra energy to compensate for the exercise and instead down regulates inefficient and generally harmful processes like random global inflammation.

As mentioned the Goldilocks zones are where you’re not forcing the body beyond what it can safely allocate to exercise in a day without causing stress in other processes. Generally though that Goldilocks zone is significantly greater than most people do in exercise in a week, but would typically fall in the zone of “moderate” exercise from a clinical point of view. This is effectively 3-6 times the expenditure of energy from rest for 150 minutes per week spread over a week for at least 10 minutes of moderately strenuous exercise at 70% heart rate per session. Most people in their 40’s or 50’s would typically find this fairly grueling, but that’s because of that homeostatic adaptation - the body resists changing its homeostasis and induces all sorts of negative experiences during the adaptation phase. Once you’ve adapted the opposite feelings present for the same reason - you begin to crave a routine of exercise because you body resists the adaptation to a more sedentary life.

N.b., This is why while exercise definitely helps lose weight, it’s primarily by managing inflammation and mood. This is why the only significant way you can lose weight over time is to reduce caloric intake materially under your homeostatic energy consumption.

I wouldn't be so sure. The brain is responsible for about 20% of resting metabolic rate, which translates to 300-350 calories per day for the average person.

300 calories is about the same as 30 minutes of zone 3 cardio (70-80% max heart rate, i.e. pretty high perceived exertion).

Most people in an exercise routine would only do that a couple times per week.

An "overactive" brain, day in day out, could add up to more than most people deliberately exercise.