Large resistive loads are not a problem during normal use. I think what you are confused about is the ‘backup power rating’ of regular batteries and hybrid inverters. During normal use (no blackout), the system can be used to power most appliances (resistive or inductive) and the grid is simply used if the load is too high.
For example, a 4.5kW hot water system can draw 3kW from a hybrid inverter & battery and 1.5kW from the grid. However, when there is a blackout most hybrid inverters can only BACKUP essential loads like lighting and one or two power circuits. See the grey column in the chart below.
Only larger off-grid inverters have the ability to power large resistive or inductive loads all the time.