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Despite existing constraints, it remains possible that up to $35\%$ of all dark matter is comprised of compact objects, such as the black holes in the 10-100\,M$_\odot$ range whose existence has been confirmed by LIGO. The strong gravitational lensing of transients such as FRBs and GRBs has been suggested as a more sensitive probe for compact dark matter than intensity fluctuations observed in microlensing experiments. Recently ASKAP has reported burst substructure down to $15μ$s timescales in FRBs in the redshift range $0.3-0.5$. We investigate here the implications of this for the detectability of compact dark matter by FRBs. We find that a sample size of $\sim130$ FRBs would be required to constrain compact dark matter to less than the existing 35$\%$ limit with 95$\%$ confidence, if it were distributed along $\gtrsim 1\,$Gpc-long FRB sightlines through the cosmic web. Conversely, existing constraints on the fraction of compact dark matter permit as many as 1 in $\approx 40$ of all $z \lesssim 0.4$ FRBs to exhibit micro-lensed burst structure. Approximately $170$ FRBs intercepting halos within $\sim 50\,$kpc would be required to exclude the fraction of compact dark matter in each intercepted halo to a similar level. Furthermore, we consider the cumulative effects of lensing of the FRB signal by a macroscopic dark matter distribution. We conclude that lensing from a uniform distribution of compact objects is likely not observable, but suggest that FRBs may set meaningful limits on power-law distributions of dark matter.