Are there downsides to larger watt inverters other than cost?
Efficiency. If the inverter operates at no load it still consumes the energy. Larger inverter -> more energy loss, even if efficiency of the inverter is the same. There is a loss in a transitor switching and loss in the magnetics, like transformer, inductor/choke. Transitors need gate driver circuit, when more transistors are paralleled the gate capacitance increases, this charge/discharge energy is wasted. If transformer is involved there is a loss due to magnetization characteristics, more iron, more loss. Same is about ferrite chokes, larger chokes -> more ferrite -> more losses.