Proto, an essential nutrient BY DEFINITION, an objective meaning not subjective, is a nutrient that is required for the body's survival and one that cannot be created by the body or not created in sufficent quantities. Fats and protein are the essential macronutrients not carbohydrates. This is fact. This cannot be disputed. Without EFA's and EAA's you will die. This is another fact that cannot be disputed. These nutrients cannot be synthesized by the body and therefor are termed ESSENTIAL NUTRIENTS. Try as you might, you cannot make the same argument for carbohydrates. The body will not succumb to death no matter how long it's deprived of carbohydrates. Again, not up for debate, it's everywhere in the studies, the medical literature, etc.
The reason to replenish glycogen stores is one of convenience and it does serve a good but not CRITICAL function. Replenishing glycogen will help your intensity remain high in the gym. If you're dieting down carbs will also help reverse the problems associated with leptin and ghrelin. When you're dieting down without carbs or on a severely carb restricted diet the body will fight back by altering leptin and ghrelin hormones as well as thyroid hormones. 1 big ~200g carb meal is enough to reverse his process and get your hormones to stop 'fighting' you. Although it's a benefit, it is not a necessity and again not an essential nutrient.
Read:
A Primer on Nutrition Part 1 | BodyRecomposition - The Home of Lyle McDonald
What I said above doesn't mean carbs are bad, not to be desired, to be avoided, provide no benefit etc. It's just that they are not essential as defined by the literature. Yes we can make arguments about how carbs are beneficial, can help bulking, etc but that's not the argument here. You had made the claim carbs were "essential for recovery and muscle growth regardless of their essential nutrient status" which is not true bc keto dieters don't need carbs to recover from workouts or build muscle.
In regards to your experiment with running no carbs there are many flaws making it erroneous to draw definitive conclusions from. Loss of Strength is not an accurate indicator of muscle loss (lacking carbs your intensity suffers in the gym making strength loss during a workout a reality, but it comes back), did you do a bodpod or dexa scan to measure body composition BEFORE AND AFTER EACH EXPERIMENT??? I doubt it meaning your claim of losing muscle just a claim. We cannot definitively say one way or another what happened without an accurate body comp assessment (calipers don't count). Patient reported diets are a huge source of error in studies and we've learned that to accurately assess intake in a study it must be done by the researchers not the patients. Patients usually over or underestimate intake. Just bc fat cals were higher than protein cals doesn't mean much, a rough estimate is 65%cals from fat to prevent gluconeogensis but it can vary slightly from person to person. You also didn't have a zero carb intake, almost all foods have trace carbs. you'd need two weeks or so just to get into ketosis meaning your 1 month run was only 2wks of true ketosis which isn't long enough to determine anything. Finally, you may be one of the few who cannot adapt to using ketones as fuel. This doesn't mean you can't run keto or that you NEED carbs for survival it just means you'll perform better with carbs (which no one argued against).
Bullshit on muscle 'swelling' increasing protein synthesis. Protein synthesis can be maximally stimulated with some protein alone, and sweeping the muscle doesn't do jack shit to growth. Ask all the people who run nitric oxide products how much mass it has gained them. Creatine drives intramuscular water storage, by your definition this means creatine is an essential supplement. Yes muscles are 75% water but water doesn't make bigger muscles, it makes bloated muscles.
Muscle hypertrophy, sarcoplasmic hypertoephy (associated with increased muscle mass) is an increase in the cross-sectional area of the muscle tissue. Water has no effect on this whatsoever.
Carbs may be a more efficient source of energy as the body won't need to turn ketones to glucose but that's not better. Some people LOVE low carb diets like keto and do better on that. It's an individualistic issue.
That Layne Norton study is irrelevant to our discussion, it's not about absorbing a days worth of protein in a single meal (if it's the one I'm thinking of). Let me ask you this, why is protein the only nutrient that can't be absorbed if taken all in one meal? What about fats and carbs? Do hose get pissed out like protein? We wouldn't have obesity if that was the case.
IF diet has a 18/6 fasting/feeding window typically. 3 or 1 meals it's the window more than anything. The warrior diet does in fact advocate 1 big meal a day. IF may not be optimal for YOU, you can't blanket statement the whole population bc your results were not great. Again BS on IF not being an optimal way to build muscle. I helped several friends set up IF diets on a bulk and they've gained a minimum of 15lbs lbm in record time.
I ask you to quantify results vs BEST results. Please how much more muscle mass will one gain with the BEST results? You're missing he forest for the trees by focusing solely on protein synthesis and missing out on net protein balance as RippedZilla pointed out. Protein synthesis isn't even the whole part of the equation and not even the most important part.