What's the purpose of a battery in a camper?
Why does a camper have a battery? You don't have a starter. If you are always connected to shore power, why do you need one? Maybe if I boondocked, but the power from a battery isn't going to do much ...
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I would have an on board battery even if I had a modern converter. I can't imagine only using my camper in a campground with power, but I'm sure there are folks that like it that way. My camper is older and I have a small battery charger, with no modern converter. As stated above, how would you run a modern refrigerator while on the road with no 12 volts? My original refrigerator and water heater didn't require 12 volt power, but when I rebuilt the camper I put in modern electronic ignition. I don't regret that at all. It is much nicer.
So to answer the OPs question, if set up properly you can run a TC without a battery, but with modern appliances you can't use them on the road without the 12 volts.
So to answer the OPs question, if set up properly you can run a TC without a battery, but with modern appliances you can't use them on the road without the 12 volts.