It's not a minor contributor though, people vastly underestimate how much exercise our species is adapted for, how much we're capable of, and just how far off from that most of us live.
It is, in quantities that are compatible with a modern lifestyle. Sure, if you're gonna run marathons every weekend, you will lose a lot of weight from that. But that's not possible to achieve while leading a normal modern life (full time employment, a relationship, children).
I think it is doable in a modern lifestyle, but that most people don't make it a priority.
Most people waste a shocking number of hours out of every day scrolling, watching TV etc, and just take it for granted as part of a "modern lifestyle", but it's just an optional way to spend time, and not very productive.
I have full time employment, a relationship, children, and manage to get our for 1hr of running almost every day. (And find time to debate with strangers on HN XD)
1h of exercise a day is great for your health, but that's still only going to be a minor contributor to fat loss. Adjusting your diet is going to have a much, much higher impact on weight loss than 1h of (moderate) exercise/day.