bill,
Maybe you just were unlucky and got a one in a million fridge/battery combo that doesn't meet your expectations? I researched many of our coach's pros and cons before we bought, and this fridge/battery/solar issue was mentioned here and there, and I did watch the Lichtsinn videos. I fully expected it to be less than perfect, but after we took it out on the road and used it, I was pleasantly surprised.
Our fridge works fine, door opened when necessary during the day for normal usage and to verify temperature. Sometimes the compressor was running when I checked it, and sometimes not. Sounds like maybe you just got a lemon, as I don't see a lot of people complaining about their factory coach battery usage as related to fridge use. Yes, some folks have opted to increase their capacity, but that's normal for many RVers. Some just like to tinker, and some just like to complain. Some like to have that extra "safety net" of battery power available. I'm planning to upgrade to lithium when the factory jars finally start to show signs of consistent weakness, but until then, I think they'll do for our purposes.
Just to clarify, during my week long adventure running the fridge 7X24, my inverter was always "on", I had the water pump set to "on" but no water usage meant no activity, the Maxx Air fan was running almost all day long on the "auto" setting during the hotter temps but would eventually shut off overnight, the propane valve was "closed/off" as it wasn't required when parked in the driveway, and my coach to chassis battery charger was plugged into an outlet with inverter power, and available to charge the chassis battery if required, but typically it only draws power for a few minutes when first plugged in to top up the chassis battery. After that I don't usually see it running. On the best sun days, I was pulling over 15A from the 3 panels when the overall power consumption load was at it's highest during the daylight hours. As stated, I did open the doors a few times a day to check temps.
That's about all I have to say on this topic. Again, YMMV.