  We re-examine the process of loop quantization for flat isotropic models in
cosmology. In particular, we contrast different inequivalent `loop
quantizations' of these simple models through their respective successes and
limitations and assess whether they can lead to any viable physical
description. We propose three simple requirements which any such admissible
quantum model should satisfy: i) independence from any auxiliary structure,
such as a fiducial interval/cell introduced to define the phase space when
integrating over non-compact manifolds; ii) existence of a well defined
classical limit and iii) provide a sensible "Planck scale" where quantum
gravitational effects become manifest. We show that even when it may seem that
one can have several possible loop quantizations, these physical requirements
considerably narrow down the consistent choices. Apart for the so called
improved dynamics of LQC, none of the other available inequivalent loop
quantizations pass above tests, showing the limitations of lattice refinement
models to approximate the homogeneous sector and loop modified quantum
geometrodynamics. We conclude that amongst a large class of loop quantizations
in isotropic cosmology, there is a unique consistent choice.
