Many battery charges aren't so efficient, while PV chargers are optimized for efficiency.
AC to DC converter is often a regulated switching power supply (which still has poor power factor, ugly harmonics.) Simple rectifier to capacitor is also ugly. I would want to add some kind of soft-start in series to avoid surge charging capacitors in MPPT.
My main objective was to access all battery charge and measurement functions of the inverter/charger, rather than sneaking around it with a separate battery charger. In the case of my Sunny Island, would require a shunt to it can see who else is charging how much. If I fed a generator into an AC coupled PV inverter, for all it knows this is another PV source.
With an inverter generator, tapping off the DC rail seems like the thing to do. It is likely charged by a 3-phase generator, less ripple.