I don't know if there is anything dangerous about induction; but I certainly don't enjoy it and have difficulty doing quality runs like hill training, speedwork or long runs. Those are the building blocks of my training and I've run poorly on induction or at very low carb levels.

Rapid weight loss is probably not a great objective either. You must take it off to keep it off, which is a life changing event, not a short term objective. You have to build your other goals with the thought of moderate weight loss.

As for the lady who was running 10 milers on low carb, that was JKMom, I believe. Keep in mind that she was eating a lot of vegetables, as well as almond butter. She ate a fairly low carb diet; but I doubt it was below 20.