Skolemization and quantifier dependencies

When we Skolemize a sentence A, we replace all the existential
quantifiers Ex1,...,Exn and the variables x1,...,xn they bind with
Skolem functions f1,...,fn whose arguments consist of only the
variables y1,...,ym bound by all the universal quantifiers preceding
the Ex1,...,Exn. This is supposed to illustrate that the existential
quantifiers (and associated variables) rely only on the universal
quantifiers. But why don't they also rely on preceding existential
quantifiers?

For example, consider the sentence (Ax)(Ey)(Az)(Ew)B(x,y,z,w) and its
Skolemization (Ef)(Eg)(Ax)(Az)B(x,f(x),z,g(x,z)). Why doesn't the last
Skolem function g have a third argument consisting of the term f(x)
which is the function that replaced y?

I have a deep feeling that I missing something very fundamental, but I
can't quite figure out what.

.