"Essential" here means something that cannot, in any way, be further removed from consideration. In this view, things that simplify the understanding and make the program more practical are not essential - they are add-ons on top of the most primitive computational model(s). You can drastically simplify the reading of the lambda calculus by giving it direct support for integers, for example - however, you now polluted the model with an additional element that you need to describe and always keep in mind. Using Church encoding lets you get integers without introducing any new elements to the model, keeping the model simpler - but yes, the implementations of programs within that model will get much more complex to read.