Side note, there's a thing called the Potato Hack [0] that proposes 3-5 day potato-only diets for short term fixes. A "potato fast" if you will.
It is a bit odd, though, that we use “going on a diet” to describe a short term change.
But I think the most accurate phrase would be that you’ve “changed your diet,” (implicitly, permanently).
I agree that it they often aren't sustainable and need to transition into a more sensible long-term diet.
It means at least two different things:
It can refer to specific planned period of eating a certain way to achieve a certain end.
e.g. Atkins diet(please look up how he died before considering this), fodmap diet , low GI diet, potato diet
It can also refer to the normal way a particular person at particular place and time in history eats.
e.g The Roman diet, Celtic diet, American Diet, French diet, Pandas diet, Neanderthal diet ,Vegan/Vegetarian diets, Kosher/Halal diets
I don't believe this matters either way, though. You shouldn't be basing your understanding of what a healthy diet looks like on the outcome for one individual. Experts in the field of human health do not believe that Atkins' diet was healthy, and that should suffice (though of course there are plenty of other unhealthy diets, some of which have problems that Atkins avoids).
I have no idea if he followed his own diet or if his diet is healthy or not, but if you have references to studies this thread is sorely lacking.