When a Growatt LF, AIMS LF, or like inverters are connected with grid input and pass-through relays are closed, the inverter is synchronized to, and operating in parallel with grid. The center tapped output transformer secondary winding of inverter is also acting as an autotransformer to provide 240/120 vac output. With no AC input neutral connection (240ac input only), all imbalanced 120vac loading on output of inverter is being carried by inverter output transformer and the 120vac power is supplied by the output transformer transforming AC input 240vac input power down to 120vac.
The reason they do not provide AC input neutral connection is they do not have any provision to check for excessive neutral current due to output transformer trying to correct for any AC input L1-N, L2-N imbalance. (other than transformer getting too hot)
If AC input neutral is connected to AC output neutral, as more transformer neutral balancing current happens, less transformer core peak magnetization range is available for inverter primary winding transfer power. In the extreme case of imbalance, the transformer can overheat without any actual inverter AC output load on inverter. The primary issue come into play when the low voltage primary side is required to transfer power for charging or AC output load supplementing. These model inverters do not provide AC output load supplementing (load shaving).
If a significant percentage of the transformer VA capability is eaten up trying to balance AC input L1-N-L2 there is less transformer VA capacity available for inverter transformer primary winding side power transfer. This can result in transformer core getting closer to saturation with a given charging load that should be no problem for transformer to handle. When this happens the current in primary side switching MOSFET's can shoot up to destructive levels due to transformer core approaching saturation.
Xantrex, Outback, and like LF inverters, monitor for the neutral imbalance current carried by output transformer. They will release pass-through relay connection to grid if AC input neutral imbalance correction current gets greater than a few amps. This allows them to have common connection between input-output neutral. To these inverters, AC input neutral imbalance is just another AC input qualifying criteria, just like min-max AC input voltage and AC input frequency range limits.
Having the extra current sensing points on AC paths within the inverter has a couple of other benefits.
Any 120vac output load current is carried directly to L-N AC input so 120vac loads do not consume transformer VA capacity during AC pass-through.
The extra AC current sensing also allows inverter to load shave and load supplementing, allowing output power to be supplemented by inverter battery power resulting in output power capability greater than inverter or AC input (as in case of generator input) is capable of alone. This also allows inverter to limit the maximum AC input current drawn which is very useful when operating from a generator to stay within limits of generator capability and with battery power supplementing allowing more AC output load than can be provided by generator alone.