However, consider the trivial case of your calories coming from poison. Not shockingly, strict equivalence is out the door.
Which is not too say it is a worthless proxy. It is quite good, actually. But it is just a proxy.
Not to say this is a myth like Chinese Restaurant Syndrome, but there is honestly a lot of evidence either way so we can't make establish a causative relationship for everyone. It is quite possible for people to have a short term reaction to salt because the hormones in charge of water and sodium balance can take several days to stablise, but again, we are unsure of long term consequences especially on an individual level.
https://www.newscientist.com/article/2101015-does-eating-mor...
https://www.scientificamerican.com/article/its-time-to-end-t...
The rest of your symptoms suggest that you are either eating too much like the guy from Supersize Me, or have more underlying health issues that require a better designed diet to heal. It's not food but how you eat.
They are equal, as anybody with rudimentary knowledge of biochemistry can tell. Modern processed food have the added benefit of micronutrient fortification so your need of vitamins should be met mostly in case you actually plan to follow that diet.
The appeal of a "balanced and natural" diet has a mostly puritan origin but its benefits are far from clear. The only proven method to delay the onset of aging is caloric restriction. Kale and supplements are mostly placebo.
As I said in a sibling post, restricting calories works. But, so does restricting grams. The same way not writing code prevents bugs. It also prevents features, so is a somewhat worthless endeavor.
Is that really true though?
The only proven harm of sugar is that it ruins your teeth. Tooth decay is relatively rare in Europe until the introduction of refined sugar. A small number of people have a hereditary condition that causes a painful reaction to the fructose component of sucrose and they get conditioned from early life to avoid all sweet foods. They tend to have immaculate teeth but are not otherwise more healthy than the general population.
However, it seems you are assuming that we have adapted to our current diet. Possible? Surely. As an argument, though, this is appealing to the incredible nature of our bodies. I'd prefer evidence.
For years, medical biologists such as Robert Lustig predicted all sorts of havoc that happens when we eat sugar and promised all of our problem woulds go away if we cut sugar from our diet. A lot of it makes good theoretical sense but experimental support is sorely lacking. Seeing his name quoted in this thread again and again makes me sad in a way because we are far from sure whether he is right or wrong.
Polyunsaturated fatty acids (PUFAs) have undergone a similar shift in reputation: Before the 2000s it was thought to be beneficial, now you have people like Ray Peat who reckons it is literally worse than sugar and saturated fat. I have a PhD in biochemistry myself and still find it difficult to choose who to listen to and what to believe, but if Vilhjalmur Steffansson can live an entire year in apparent good health eating only meat then the human body has to be more forgiving than we assume.
On the sugar front, is the evidence really lacking? Taubes' book referenced tons of ancient studies that showed support. Anecdotally, I have yet to meet someone that was not benefited by halting soda.
I said that I am not interested in halting research in any direction. It is likely, to me, that there are interactions involved and this will require study. I have yet to see anything that vindicates sugar, though.