It's not failures but energy dependency that limit its use in RVs. Or - used to limit. You will be replacing the dependency on reliability of propane fridge with dependency on daily charging (when offgrid). Maybe this will change in some years from now, with more Li batteries, so that you could (at least) spend a weekend without having to run a generator, but then the word "cheap" needs to be redefined. Motorhomes are more "tolerant" to 110V fridge due to alternator wiring, but the OP has a TT.
Another thing that I observed (other than being not quite cheap, in my case suitable 11 cu.ft model is +$500 plus inverter), is that most people with 110V fridges either camp on hookups or are doing short weekend trips. One of few exceptions is Mr Wiz here, with 600-something watt solar (sill has to run a generator occasionally, but he is fulltiming, different scenario).