Observed infrared (IR) excesses indicate that protoplanetary discs evolve slowly for the majority of their lifetime before losing
their near- and mid-IR excesses on short time-scales. Photoevaporation models can explain this ‘two-time-scale’ nature of disc
evolution through the removal of inner regions of discs after a few million years. However, they also predict the existence
of a population of non-accreting discs with large cavities. Such discs are scarce within the observed population, suggesting
the models are incomplete. We explore whether radiation-pressure-driven outflows are able to remove enough dust to fit
observations. We simulate these outflows using CUDISC, including dust dynamics, growth/fragmentation, radiative transfer and a
parametrization of internal photoevaporation. We find that, in most cases, dust mass-loss rates are around 5–10 times too small
to meet observational constraints. Particles are launched from the disc inner rim, however grains larger than around a micron do
not escape in the outflow, meaning mass-loss rates are too low for the initial dust masses at gap-opening. Only systems that have
smooth photoevaporation profiles with gas mass-loss rates >∼5 × 10−9M yr−1 and disc dust masses <∼1 M⊕ at the time of
gap opening can meet observational constraints; in the current models these manifest as EUV winds driven by atypically large
high-energy photon fluxes. We also find that the height of the disc’s photosphere is controlled by small grains in the outflow as
opposed to shadowing from a hot inner rim; the effect of this can be seen in synthetic scattered light observations.