I think 7 watts is possible, and if so that is damn good. My Renogy 12V 2000W HF inverter idles at .9a 13V = 12 watts. Same for the Renogy 12V 3000W HF. The Renogy 12V 3000W LF with fan on idles at 2.23A 13.1V = 29 and fan off is 1.67A 13.1V = 20 Watts.
The LF inverter also has grid charging and auto transfer capabilities that these HF inverters do not. That is valuable feature you get for the extra watts.
The question is, do we have to pay that 20W of overhead once a load kicks in? I tested a 250W heat lamp that draws exactly 250W on grid power and 258W on inverter due to higher AC voltage. When running on the inverter I get 21.9A 12.57V (small test battery) = 275 Watts. So the inverter is 93% efficient in this case and that includes the 20W of overhead power. In other words, when you have a substantial load, that standby power gets rolled into normal DC to AC inverter losses.