Yup, new solutions have new problems.
I have done some traveling in my Golf with a compressor fridge with only the car battery. No problem running down the road, but some days the battery would be dead in the morning. I travel with a lithium jump box, so I would just use this to start my car and then travel on. I now travel with a smaller fridge and a lithium battery to power the fridge. Kind of an expensive solution but it works, and I also use the battery for the electric motor for my fishing kayak. When I am not traveling I use an 80 watt solar panel to charge the battery.