I suppose it would all depend on how much you sit and wait or not, and how much you are home and don't need the fridge.
Not quite the same as a real fridge, but I have a Coleman Thermoelectric cooler that runs on either 12v or 110 AC (lots of room, stands upright like a fridge or down like a cooler, only $99 or so).
In my case, having the dual power has been priceless. I regularly hook it up to 110 when home or at my shop and just leave everything in there instead of transferring to the house or shop fridge. It's light enough too that I can bring the whole thing in if I want.
I use it on 12v when running down the road or for short periods when loading, unloading, or fueling etc, even quite often for an hour or two with the engine off with no real noticeable effect on starting.
In current weather, I can leave it unpowered overnight and still have cold contents in the morning. Some guys build an insulated jacket or thin wall insulated box to further protect it when not powered.
Once I have separate batteries for powering accessories and an inverter, I'll be able to run it when just sitting and without shore power.
So, I'd say yeah, the dual power is worth it, though I know having that option in a real fridge with condenser, like Dometic and others sell, makes them more expensive.