10 Amps is not that much on 12 volts.
I think that the problem for the users who want to run their fridge is the voltage drop from the alternator to the trailer battery
To have low voltage drop the connections must be good and the wire gauge large.
there is a dedicated connection for the 12 volt for power to the trailer.
There is a separate path for the brakes
so that is not a concern.
In my setup I have a 30 amp breaker that feeds a 30 amp relay that cuts off the circuit with the key off.
The breaker is there to protect the wire.
The 10 gauge wire I ran to the trailer socket is about 18 ft long and the wire to the PD4045 in the trailer is about 12 ft long.
I feed the buss on the PD4045 with a second 20 amp breaker/fuse from my terminal strip.
So we have 30 ft of #10 wire which has a resistance of 0.048 ohms.
Since the voltage drop E=IR 10 amps X .048 ohms = 0.48 volts
So we are talking about 1/2 volt drop best case.
Most alternator regulators will run about 13.75 volts at the battery terminals long term average so we will be looking at 13.25 volts at the PD4045 (best case) which is the floating voltage of a fully charged battery.
If you start with a charged battery you should be able to pretty much the maintain the battery since the refrigerator should not have to draw power all of the time.
I suspect one problem may be the circulation of air past the cooling fins of the refrigerator.
The normal circulation is by convection up and past the works in the back of the fridge.
Does anyone know what the airflow across the trailer does to the "normal" convection flow? I don't.
Most larger trailers have a vent on the roof and the intake on the side and the path is straight up and out.
With the smaller fridges the vents are both on the side and my guess is that the airflow along the side of the trailer is quite confused and perhaps the addition of a small 12 volt fan to make the airflow certain might be a worthy addition to insure proper flow.
I know on my Norcold 1200 with a side vent at the top and bottom due to it being mounted in a slide out needs additional fans to cool properly especially in the 100*F temps we have in Mobile AL. (AKA LA).
So big wires, heavy connections, clean tight plugs and sockets, and add a fan for the airflow.
If the unit cools properly it will cycle on and off giving the battery a chance to charge when the voltage goes over that 13.25 volts.
Personally I have a compressor type Norcold 704DE that does not challenge the wiring at all.
I use the above monitors for the power for both AC and DC ant they let me see what is going on quite well.