Those 4 hours don't mean wall clock time, they mean it takes 4 hours to discharge the battery at its maximum discharge rate.
In other words, the battery would bridge exactly 4 hours of 0% power generation. The moment you have more than 0% power generation but still less than 100%, the battery will last more than 4 hours of wall clock time.
The battery will mostly be drawn down at a time of much less than peak demand, so will provide power for longer than 4 hours. But it will be available too for when demand peaks above generating capacity.
It is usually a mistake to overbuild batteries. The money is better spent on PV panels, wind turbines, and grid tie-ins and, eventually, other storage media.
