You may look up Pellagra. It is, of course, not a threat in a modern western society, but it used to kill people. Not even an experiment, but something that happened in nature. Yes, there are reasons to consider EFA deficiency.
Would a person die horribly if good sources of fat and protein are abundant, but glucose is not? I don't think so.
Glucose deprivation leads to disease.
Again, I would like to see some source. What particular diseases? There are whole groups of peoples (i.e. Inuit, Maasai) who were eating diets almost entirely lacking glucose before Western foods became available to them.
Do you realise, at least, that the body can produce it's own glucose from the excess fat (Gluconeogenesis)?
A person eating nothing but fat and protein will have chronically elevated adrenalin and cortisol, will prematurely age, and be more prone to various degenerative diseases.
You could at least look up the first line of a Wikipedia article? Tryptophan is an essential amino acid.
It can be caused by decreased intake of niacin or tryptophan,[1] and possibly by excessive intake of leucine.
Anyway, in the absence of any sources there's not much I can gain from this discussion, unfortunately.
Sugar/starch is more rightfully considered essential because glucose is clearly the preferred fuel for animal cells. Glucose deprivation leads to disease.