  Two-neutrino double-beta ($2\nu\beta\beta$) decay has been used to constrain
the neutron-proton part of effective interactions, which in turn is used to
compute the nuclear matrix elements for neutrinoless double-beta decay, the
observation of which would have important consequences for fundamental physics.
We carefully examine $2\nu\beta\beta$ matrix elements within the proton-neutron
quasiparticle random-phase approximation with nuclear energy density
functionals. We work with functionals that are fit globally to
single-beta-decay half-lives and charge-exchange giant-resonance energies, but
not to $2\nu\beta\beta$ half-lives themselves, to evaluate the $2\nu\beta\beta$
nuclear matrix elements for all important nuclei, including those whose
half-lives have not yet been measured. Such a comprehensive evaluation in large
model spaces without configuration truncation requires an efficient
computational scheme; we employ a double contour integration within the finite
amplitude method. The results generally reproduce the nuclear matrix element
extracted from half-lives well, without the use of any of those half-lives in
the fitting procedure. We present predictions of the matrix elements in a total
of 27 nuclei with half-lives that are still unmeasured.
