Laco, I like easy also. In your case you “may” be able to save a little 12-Volt power by eliminating the inverter inefficiency since it’s fed from 12-Volts, but since inverters are so efficient, it won’t make much difference anyway — maybe a few Amps which your alternator should handle easily. I say “may” because specs show a different amount of power on 110 AC versus 12 VDC. It’s so small that’s it’s not worth worrying about.
In any case I agree with most of you and wouldn’t run a generator just to power the fridge. If the generator was being run anyway, that’s different.
Personally, for smaller rigs, I like the newer 12-Volt compressor refrigerators that use very little power. Many Class Bs have gone that route and eliminated propane for compact fridge.
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