We want invariance under base change because we want to be able to pull back covering sieves. This is pretty much the entire point of a Grothendieck topology. Without the base-change axiom, we only have the local converse, if the pullback by every map of a covering sieve of a sieve S is a covering sieve, then S is a covering sieve. Base-change corresponds to the ability to pull back open covers of topological spaces by preimages of continuous maps.