  We constrain the Hubble constant H$_0$ using Fast Radio Burst (FRB)
observations from the Australian Square Kilometre Array Pathfinder (ASKAP) and
Murriyang (Parkes) radio telescopes. We use the redshift-dispersion measure
(`Macquart') relationship, accounting for the intrinsic luminosity function,
cosmological gas distribution, population evolution, host galaxy contributions
to the dispersion measure (DM$_{\rm host}$), and observational biases due to
burst duration and telescope beamshape. Using an updated sample of 16 ASKAP
FRBs detected by the Commensal Real-time ASKAP Fast Transients (CRAFT) Survey
and localised to their host galaxies, and 60 unlocalised FRBs from Parkes and
ASKAP, our best-fitting value of H$_0$ is calculated to be $73_{-8}^{+12}$ km
s$^{-1}$ Mpc$^{-1}$. Uncertainties in FRB energetics and DM$_{\rm host}$
produce larger uncertainties in the inferred value of H$_0$ compared to
previous FRB-based estimates. Using a prior on H$_0$ covering the 67--74 km
s$^{-1}$ Mpc$^{-1}$ range, we estimate a median DM$_{\rm host} =
186_{-48}^{+59}$ km s$^{-1}$ Mpc$^{-1}$, exceeding previous estimates. We
confirm that the FRB population evolves with redshift similarly to the
star-formation rate. We use a Schechter luminosity function to constrain the
maximum FRB energy to be $\log_{10} E_{\rm max}=41.26_{-0.22}^{+0.27}$ erg
assuming a characteristic FRB emission bandwidth of 1 GHz at 1.3 GHz, and the
cumulative luminosity index to be $\gamma=-0.95_{-0.15}^{+0.18}$. We
demonstrate with a sample of 100 mock FRBs that H$_0$ can be measured with an
uncertainty of $\pm 2.5$ km s$^{-1}$ Mpc$^{-1}$, demonstrating the potential
for clarifying the Hubble tension with an upgraded ASKAP FRB search system.
Last, we explore a range of sample and selection biases that affect FRB
analyses.
