Even without a battery people usually choose hybrid, which can function on and off grid.
Also to be honest I'm mostly looking at larger inverters so maybe that colors it. Not many users here need 24,000 watts continuous outside a commercial context, for instance, so an inverter with that as an input but 12,000 watts continuous AC output doesn't seem weird since part of the 24,000 watts DC can be sent to the battery.
Then it's just a race to pay back the panels, which are most of the cost, so undersizing the inverter is wasing energy and leaving money on the table.