You can definitely get equipment that can do symmetrical input/output, but if you actually model out the supply and demand curves on the system it's not usually going to be worth the extra up front expense since peak input is a small portion of the day and that extra hardware will mostly sit idle.
For that matter people often design systems where peak input can't even be accepted by the inverter and the extra power is just wasted, because it's more valuable to have a steady input over a long period than to maximize the daily peak.
I know multiple people with solar and have discussed their specs with them extensively. Zero of them have inverters or microinverters sized below the theoretical max of their array.
Are you thinking of a purely off-grid setup without actually saying so?
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.