Back when I was doing high intensity interval training in college I would regularly hit ~2k calories burned a day. Few things satiate the kind of hunger that gives you like a burger
If you're actually trying to manage your weight, do not increase your physical activity. Reduce how much you eat.
Most sites say running burns around 60 Calories/km or 100 Calories/mile. The average person burns 2,000 Calories a day by existing. If you ran a 10k every day, then you'd be using 2,600 Calories a day.
The difference in effort between "existing" and "runs a 10k every day" is massive, but the difference in Calories burned is equivalent to a large fry from McDonalds. So would you rather run a 10k or just take the fries out of your order?
I mean, it's weird to encourage people not to increase their physical activity if they're trying to manage their weight.
While it's true you can't out-train a bad diet, exercising, even for just 30 minutes every other day will go a long. Running a 5k will take about half an hour depending on your fitness level and will burn a good 350 calories or so, more if you're overweight. Do that 3 times a week and that's the equivalent of a about 2 meals you've burnt off (or one really unhealthy meal). Plus getting outside and exercising is good for your mental health.
And then comes the fun part where your body, built for pure energy efficiency and nothing else, will try to offset burned calories by subconciously moving less throughout the rest of the day
Physically I agree with you, but psychologically it is much easier to control what I eat when I regularly go to the gym because when I work out and eat too much it feels like I am wasting my time there. So even if I only burn 300 kcal, I feel like I am taking care of my body and pay more attention to what I eat over the day.