  Given a group G, we consider its classifying space for the family of
virtually cyclic subgroups. We show for many groups, including for example,
one-relator groups, acylindrically hyperbolic groups, 3-manifold groups and
CAT(0) cube groups, that they do not admit a finite model for this classifying
space unless they are virtually cyclic. This settles a conjecture due to
Juan-Pineda and Leary for these classes of groups.
