On EHU, no reason apart from it might be a bit noisier than the purpose RV fridges.Is there any reason why you can't use a small household domestic fridge ?
but when mobile they are mostly 240vac so you will need a 240v inverter running off your 12v system..... (large enough to handle the compressors inrush current, normally 3x times the running current)
at this point is where you will run into problems as the Mains compressor is not low-power as-such and will suck power out of your leisure battery. . . . . so you need a large battery bank & Inverter.
The Dometic and other purposed 12/240 RV fridges have low power compressors that are designed to run quiet, off 12v or 240v and efficient.
3way fridges are great too . . . but if on gas it has to be outside, its fine on 240 EHU but not very efficient running off a 12v battery bank as the can draw around 6ah . . . .
so . . .
EHU = no problem with anything.
12v = 3way fridge about 6ah draw
12v = thermo electric cooler box about 3ah draw
12v = compressor fridge about 1.5ah draw cycling on/off as reqd