Ideally, yes, but the problem with simply running the appropriate gauge wire from the battery to the inverter is that the proper gauge wire may need to be a fairly large gauge. Look at it this way. If you need to supply 120VAC at 2A on the AC side, it will require cable on the DC side capable of carrying 10X that current or 20A in this case. As the current and the distance increases, the required gauge increases as well otherwise the voltage drop will be too great and the inverter will get a lower voltage on the input side....
I agree that it should be a fused line, regardless of how it's terminated to the inverter. I disagree, however with the rest of what you have said. If you're creating a permanent home for the inverter, find the location you want for your inverter, then run the correct gauge wiring for the distance.
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I would modify your statement slightly to "If you're creating a permanent home for the inverter, find the location you want for your inverter as close to the battery as possible, then run the correct gauge wiring for the distance."
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