Battery wiring is often a problem causing too much voltage drop at inverter input terminal.
The more voltage drop to inverter DC input, the more current the inverter must draw from battery for the same AC output load.
A 3kW, 12v inverter is on the verge of being impractical due to 12v inverter systems having so little margin for voltage drop tolerance. Problem is usually compounded as an inexperienced user not knowing they should not be buying a 12v, 3kW inverter will also be less likely to deal with the extremely high battery line currents it will be creating.
On 12v systems, a fuse needs to be used instead of circuit breaker on DC input due to most breakers having too much series resistance because of their short circuit detection magnetic trip coil resistance. High current breaker with short circuit detection will have about 4-5 milliohms of series resistance.
At 5 milliohms and 200 amps, there will be about 1v drop just across breaker. A quality fuse will be less than 1 milliohms of series resistance.