Trying out a brand new Phoenix 12/250 on the test bench. Hooked up 12V from a lead acid battery though a 30A blade fuse, 10mm2 cables.
It has no problems running lights.
Next I hooked up a small fridge, usually draws about 70W, so I expected it to be with a good margin to the inverter's max.
Then, when switching on, a short brrr and then a snap from the fuse.
Manual seems not to recommend a proper fuse, only that it internally has a 60A, but I like to have fuses close to the battery.