In the discussion of the Born Oppenheimer approximation, we think about the electron eigenstates as a function of fixed nuclear positions $R$. It is then assumed that the nuclear positions vary slowly, so that the electron dynamics can be considered adiabatically following the eigenstates $|\psi(R)\rangle$.
My question is, why is it justified to assume the nuclear coordinates fixed? They are subject to quantum fluctuations. When we consider a diatomic molecule for example, we can approximate the ground state of the nuclei as a rigid rotator. The nuclear coordinates are completely delocalized in the angular dimension, even if the modulus of $R$ has small fluctuations.