I took a look at the specs for the Prosine 2.0. With a surge capability of 4500 watts, at a low battery voltage of 10.5 volts the surge current into the inverter, assuming 90% efficiency (probably less), will be 475 amps, more then justifying the 4/0 cable. My chart says 4/0 is good for 335A continuous. Since the inverter is rated at 4500 watts they are obligated by the safety agencies (read UL) to specify a cable at least that size, probably more like 350 MCM.
With a 2000 watt rating, the minimum wire size should be at least 2/0 (211 amps). This is for safety to keep the wire temperature to a safe level to prevent fire and contact burns. I would not wire with anything less, and think their recommendation for 4/0 is prudent. I know it’s a pain, but better safe then sorry.
They should have taken the time to explain this to you. It’s incorrigible that they would leave you with the impression they did. The large wire size is to keep the wire temperature to a safe level (so your boat doesn’t go up in flames) if there is a problem with the inverter or with a load the inverter is powering. Current = heat in wiring, the trick is to keep the heat to the minimum possible.
There are two types of fools...
One says this is old, and therefore good..
The other says this is new, and therefore better...