A bit of simple maths will show you that if your converter is 100% efficient then the battery current required at 3000W output will be 250A.
Semiconductors to reliably handle this current are big and expensive! Never mind the other components. For example, a volt drop of 1V in the semiconductor will loose 250W! So the efficiency will be well short of 100%.
This is why inverters to produce power in the region of 3kW generally work at much higher input voltages, probably 48V or at least 24V.