That's a great approach if the person is disciplined and motivated, but chances are if they are already overweight, they are not very disciplined and not very motivated. I lost 50 pounds mainly by changing my diet, plus a little bit of cardio every day. After that, it was much easier to do 30-mile bike rides, hundreds of pushups, etc. because I had the energy to pursue those things and had slowly built up the habits of eating right and exercising on a regular basis.
For me, the baby steps approach worked really well. I'd agree that starting out with strength training and longer cardio sessions would be great, but that's the approach most people take, and most people quit because it's too hard to keep up that big of a change in their life.