Because solar panels are current limited and batteries can give up all their energy in an instant.
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MPPT is designed to squeeze out the maximum possible DC power from the DC source (PV modules) with a large fluctuation of output voltage. The MPPT would draw as much current as possible to achieve the biggest power output. Hence it will try to get the maximum power from the battery, which it's capable of providing each moment. Compared with the car battery operation, it would be a constant "Crank mode" of the starter.
On the other side, each inverter is limited by its nominal power. If it tries to process more DC power than it's designed, it will have a "plateau" where the AC output wouldn't further grow. E.g., like, in the situation with a 10kW solar array connected to the 5kW inverter.
Hence the MPPT inverter would work safely with batteries only on one condition: the battery should be able to provide the entire nominal power of the inverter for all the time of operation of such a system. E.g. for a 5kW inverter, the battery should be able to give out AT LEAST 5kw of power constantly during its entire time of operation. In such a case, the inverter would constantly operate in a 5kW "Plateau mode," and those 5kW would be constantly drawn from the battery (regardless of its depletion) and converted to the 5kW AC (minus efficiency factor) on the inverter output.
That would be true for grid-tied inverters. For off-grid - the power output (and the DC input) would be dictated by the AC load.
There are some inverters (e.g. Sunny Boy SMA-5000) allowing to choose of MPPT vs. non-MPPT mode for the DC. They are certified for DC sources with content voltage (like batteries), however, the batteries are not mentioned directly.