Most of your calorie deficit comes from your Basal Metabolic Rate and it's very hard to excercise enough to achieve a calorie deficit. While strictly possible, practically speaking for most people the only term you control in the equation, if any, is the intake.
> it's very hard to exercise enough to achieve a calorie deficit
I don't know what your definition of "very hard" is, but you can burn anywhere from 100-150 calories for every ten minutes of high intensity work (more calories burnt as your weight increases, for the same level of intensity). So 30-40 minutes a day will get you 1500-3k calories over five days depending on your starting weight. Unless you're eating 3-4k calories a day you will very likely lose weight with that level of activity.
Your last sentence is so wrong I'd say it's dangerous. The hard truth is a lot of people "go to the gym" for two hours every day, but end up doing 30 total minutes of low-intensity work. That might be a nice social activity but there is very little physical benefit. Or they go on a 15-minute walk that doesn't get their heart rate up. Again, if you want to do it because it's enjoyable I'm all about that (I love walking my dog). But don't fool yourself or lie to other that you're doing something for your health, because you're not.
Put bluntly, most people just don't work out hard enough. Spike your heart rate, sweat, lift heavy weight and have sore muscles. If you're trying to lose weight, and you don't break a sweat and you're not out of breath, you're not going to get where you want to go. Do a group class like OTF or CrossFit if you aren't sure what to do or want the supervision. But you have to be uncomfortable (not in pain, which is an important distinction) to change your body.
> Put bluntly, most people just don't work out hard enough.
Yup. Most people won't. Certainly not every day. 100 calories for ten minutes of excercise means that you're undoing your one workout you did this week on your first soda.
I think that the threshold of discipline for maintaining that kind of training schedule is higher than the discipline required to cut your calorie consumption. While the math correctly says you can excercise enough to offset any amount of bad eating habits, realistically forcing yourself to excercise is a similar task to forcing yourself to stop eating ice cream or whatever your vice is.
I also think that, as you pointed out, you burn so few calories while doing the type of low intensity excercise that amateurs, myself included do, you're really getting very little measurable impact on your calorie needs. So it becomes an act of self deception: oh I can cheat but I'll make up for it. You won't!
