"Exercise" is a bad way to lose weight because what is traditionally considered as exercise is 30 minutes to 1 hour of high intensity activities. If you live a sedentary life, exercise isn't going to help.

Passive exercise, that you do throughout the day, though, is a great way to expend calories. Walk more, bike for transport, use a standing desk, etc. That's the difference between 1500 calories and 2200.

I don't think that's as universally agreed upon as you claim. I know of plenty of women who struggled to lose weight via diet and cardio, and then turned things round when they started eating high protein and lifting weights.

Diet + cardio with no strength work can put people into 'gotta make it through this famine' mode, where their metabolism slows right down to eke out the stores as long as possible.