I should still exercise for other reasons, but not for losing weight.
I struggled for years to get my weight down. Then just walking every day to ensure I was at 10,000 steps managed to move the needle in a meaningful way. Over a few years that turned into running a few times a week, which turned into running daily. In the beginning I had already been counting calories and the calories I was burning walking whatever it took to get from my normal amount to 10k (varied each day) was not enough to justify the weight being lost when compared to calories consumed. It should have been much slower.
Part of this might also be about how exercise generally leaves you feeling pretty good, usually better than after a day that is spent entirely sedentary in my experience. A lot of people crave the instant satiating feeling of eating. Eating often feels good. The exercise might then help by replacing the "make me feel better" feeling that food might give you, leading to you swapping out "unnecessary" feeding and lowering your caloric intake in the process.
My partner swears their caloric cravings increase disproportionately after workouts and feels strongly that reducing food intake has helped them maintain weight far more than exercise. There are probably some genetic components to this (according to our 23andme data, we have very different genomes).
Then what happens when they don't see results is they proclaim it does not work and drop exercising altogether. What they did not do is stick long enough to actually see the results.
Exercise is to keep your healthy and to improve your internal regulation. It is to keep you feel well so that you don't feel compulsion to eat more just to feel well.
How many calories does extra muscle mass burn daily?
When we're talking about slowly gaining weight over time as the OP did, even if muscle only burns a little more energy than fat that could be enough to tip the balance.
Most people that eat a lot and don't seem to gain weight are simply not eating that much calorically or exercising a lot. When a more sedentary lifestyle kicks in they generally begin to align more with the general population.
https://www.gq.com/story/body-types-explained-ectomorph-endo...
But the other issue is, given you're a normal-sized, metabolically healthy 10 year-old, will developing a lifelong habit of regular exercise and a generally active lifestyle keep you from ever getting fat in the first place? I don't know that we have any kind of long-horizon, longitudinal research to demonstrate one way or another empirically, but mechanistically, it sure seems like that should be the case, and you can look at manual laborers in developing countries, the Amish, any serious lifelong athletes in sports where being maximally large is not advantageous on its own, as existence proofs that this should help.
I think the comment you're responding to was really asking about the latter scenario. It's not, okay, you spent the last 20 years gaining 30kg, well how active are you now? The question is how active were you over the entire course of the last 20 years? Because it's likely that if you were sufficiently active, you wouldn't need to lose weight at all, and the question of exercising for losing weight would be irrelevant.
Exercise help in much broader ways than just the amount of calories burned on the spot. Take weight lifting for examples, it increases your lean mass, which means it increases your metabolic rate, which means you can eat more and not gain fat. You also spend more calories on your resting days to rebuild your muscles, &c. exercising also tend to curb appetite
In school I used to go to the gym every day for 45mins at lunch, and box 5/6hrs a week, from 14y/o. The last 3/4yrs I climbed 3/4x a week and the last 2 of those I also ran 3/4x a week up to ~40km/wk, albeit inconsistently around my 9-5 and part time uni course.
Every time I cut out one of the sports I enjoy, I am drastically less hungry. Yes, a 5km run might burn ~300cals, but if I'm so hungry I eat a whole extra meal, I'm generally more likely to gain weight. Same for lifting weights, but even moreso - if I go and hit a 200kg deadlift PR I'm going to be hungry the next day, but that 1-2hr gym session maybe burned 100 calories at most. Exercise for weight loss is only useful if "calories in" stays the exact same, and even then it would be way less effort to reduce "calories in" and not exercise (if weight loss is the only goal).
The point at which this stops applying is excessive cardio, ie running 40km+ in a week. That will pretty much always result in a caloric deficit for me, because at that point I'm forcing myself to eat enough food to recover (rather than having to force myself not to overeat). Most people exercising to lose weight (rather than for enjoyment, to push themselves/prove something, or to win a race) don't want to exercise. If you have to commit 6hrs a week to cardio to see any effect, 99% of people aren't interested, so I'd imagine they fit into the "not excessive" category where exercise might make them want to eat disproportionately more than they burned.
Controlling "calories in" (which will guarantee weight loss, as far as the laws of physics are concerned) is always going to be the easiest path to weight loss.