Cholesterol is synthesized by the liver, in sufficient quantities: https://www.sigmaaldrich.com/technical-documents/articles/bi...

believe it or not, by your definition carbs are also essential, it’s just that the body can produce them

Protein -> carbs by gluconeogenesis

Isoleucine and phenylalanine are exclusively ketogenic and produce ketone bodies.

Leucine can be used to synthesize fatty acids in adipose tissue.

The only 2 fats that we really need are omega-3 and omega-6, but not in huge amounts, thankfully, both not from meat.

Point is, one can more readily survive without a major source of fat or carbs.