What the grandparent's post is highlighting is the physics of this system is that the difference in weight is proportional to calories in - calories out. It's important for people to reduce calories in by modifying their diet. No one is disagreeing with this. However individuals committed to reducing weight can put in some time to increasing calories out (often by cardio activities such as jogging/running/cycling/swimming).
It just doesnt follow to say "you cannot outrun a bad diet" followed by "the base metabolic rate is the primary means of weight loss". There is tons of evidence that exercise is exactly what increases your base metabolic rate! Here is just one study:
"Resting metabolic rate (RMR) is the largest component of the daily energy budget in most human societies and, therefore, any increases in RMR in response to exercise interventions are potentially of great importance" [0]
If RMR is the most important thing to reducing weight, exercise is the most straightforward way to improve RMR and reducing weight. But I wont make this reductionist claim; clearly diet is also important.
Exercise can be very helpful in reducing weight; it's simple physics of increasing calories out. My most successful friend losing weight changed both his diet and increased exercising to about an hour a day. He not only shredded 30-40 pounds, but gained from the additional benefits of higher resting metabolic rate, increased cardio health benefits, reduced stress, and felt like he had more energy with fewer coffees. The quick weight loss he felt meant he didn't have to have a yearlong slog waiting to see results, making the process all the more rewarding which significantly helps for some people's psychology. Sure it sucked in the beginning, but his life was unbalanced and he committed to making big changes.
It's almost cheating to exercise with improved diets; imagine if you were keto eating salads and still able to remove "chocolate bar debt" from the past by 30 minutes to an hour of activity a day followed by increased RMR for the next 24 hours.
Bad diets are bad. Complemented with exercise you can improve your metabolic rate which will give you long term weight loss and health benefits.
At an average walking speed of 2.8mph, that's 4.6 hours of walking. The average American adult walks around 2.5 miles per day, mostly indoors trips between rooms. The American knowledge-worker or automobile-dependent suburbanite will tend to have a lower average.
Jogging / long-distance-running tends to be about twice that fast, or 2.3 hours of activity. Per day. Ten percent of their lives, running. Most people don't come anywhere close.
That's not really true. When I ran 150km/week, I didn't have to worry much about what I ate. A couple of years after having some surgery, I'm only managing about 50km/week, and I have to be much more careful.