Confusion in unit cells of crystal system
First, a note: the classification of crystal systems, or the reduction of possible lattice types into primitive Bravais lattices, has nothing to do with “space available” or “hindrance”. It is purely a mathematical property having to do with the symmetry of the lattices.

To answer your question, the base-centered cubic lattice is not a Bravais lattice, because it is equivalent to a simple tetragonal lattice: