Lowering your BMI from 31 to 24 by cutting fat makes you healthier and increases your expected lifespan (regardless of whether or not you exercise), chopping off your legs does not.
See, your goal is not just to lose weight. Your goal is to lose fat. Your body will burn a hell of a lot of muscle if you just sit still and not eat.
And becuase you're burning more muscle than fat, you're even going to lose more weight. Hooray!
For added bonus, you can lay in bed all day so that you lose bone density as well. Even more weight loss even faster! So much better BMI. Much healthy and awesome.