Maybe you know something particular about metabolic treatments. But if this is just a structural argument from more or less first principles, I think it's structurally weak. There's no reason to assume that your body's tolerance to starvation is the same as, or poorer than, the cancer's tolerance to starvation.

For example, chemotherapy is poison, just poison that is hoped to poison the cancer much more strongly than the patient. But it always hurts the patient.

Another broader example, fevers are bad for you. But in many situations, they're worse for a pathogen that has infected you, so your body tries a fever in response to some immune observations. This is why you should generally not treat a mild fever, unlike a too-intense fever. Not medical advice, I'm not a doctor.

But maybe, unlike me, you have specific knowledge of the medical issues and you have more-specific reasons to argue that metabolic attacks can't work on cancer?