  In simple models of galaxy formation and evolution, star formation is solely
regulated by the amount of gas present in the galaxy. However, it has recently
been shown that star formation can be suppressed by galactic dynamics in
galaxies that contain a dominant spheroidal component and a low gas fraction.
This 'dynamical suppression' is hypothesised to also contribute to quenching
gas-rich galaxies at high redshift, but its impact on the galaxy population at
large remains unclear. In this paper, we assess the importance of dynamical
suppression in the context of gas regulator models of galaxy evolution through
hydrodynamic simulations of isolated galaxies, with gas-to-stellar mass ratios
of 0.01-0.20 and a range of galactic gravitational potentials from
disc-dominated to spheroidal. Star formation is modelled using a
dynamics-dependent efficiency per free-fall time, which depends on the virial
parameter of the gas. We find that dynamical suppression becomes more effective
at lower gas fractions and quantify its impact on the star formation rate as a
function of gas fraction and stellar spheroid mass surface density. We combine
the results of our simulations with observed scaling relations that describe
the change of galaxy properties across cosmic time, and determine the galaxy
mass and redshift range where dynamical suppression may affect the baryon
cycle. We predict that the physics of star formation can limit and regulate the
baryon cycle at low redshifts ($z \lesssim 1.4$) and high galaxy masses
($M_{\ast} \gtrsim 3 \times 10^{10}~M_{\odot}$), where dynamical suppression
can drive galaxies off the star formation main sequence.
