It is thought that our bodies compensate to regain calories expended via exercise in other mechanisms (through hunger, metabolism adjustments, and other mechanisms.)
But monitoring calorie intake vs expenditure really does make a difference. I went through multiple cycles of controlled 10kg+ weight gain and loss, and I must say that just by walking extra couple miles a day while enforcing the calorie limit can make all the difference.
What doesn't work for weight control is just doing more sports - this is easily compensated by hunger.
Because their bodies compensate by eating more and they are surprised they are not losing weight and they think that exercising does not work.
Which is completely wrong way to look at it. You want to get healthier to lose weight not lose weight to get healthier. And exercise is one of the best ways to help you get healthier even if it does not directly and immediately lead to losing weight.
If you combine calorie deficit, a body that is in dire need of energy, high fasting insulin leading to inability to reach into fat stores, underdeveloped mitochondria making burning fat even more difficult, your result is body that prioritises burning protein for fuel.
If you exercise not only the body gets signal to preserve the tissue and muscles that are being loaded, but also keeps building mitochondria that are necessary to effectively burn more fat.
I would hope people exercise to a limited extent anyway, to the extent their bodies will try retain a baseline level of muscle-stength needed day to day.
As you've read on my other comment, I lost 20kg over 6 months on a low carb, low sugar, higher protein diet. I started gyming about 4/5 months in and I personally attribute this gyming with a chain-reaction that led to me putting the weight back on and am now in a much worse position health wise, even muscle wise. This all due to practical reasons, such as increased appetite which upset the hard-fought dietary and hunger equilibrium I reached.
Exercising too is I'm sure definitely better but I feel is way more difficult and sets many, on the weightloss journey, up to fail.
Regular exercise causes people to be hungry and compensate for the additional activity. That's normal.
But I probably am feeling and healthier than I would if I wasn't running.
As an example, my body got rid of all the skin folds. I should have flappy loose skin around my belly and I should have old looking skin on my face. Instead my body, being much healthier than if I was just restricting calories, is able to break up and use that extra tissue and got rid of all that skin naturally.
I learned that a doctors evaluating people who lost significant amount of fat can guess pretty correctly at the method the person used to lose the weight just based on how their skin looks like.
I went down from 93kg to 78 and then from 90kg to 78. I didn't go for low carb or sugar, just ensured enough protein and overall calorie deficit. Right now I am just carefully float around 80 kg.
This, and moderate excercise (kettlebells, some weightlifting, walking) made things relatively easy as I just made sure I stayed in an overall deficit.
One more point: it's the running weight average matters, not daily measurements.