It's not a bad of engineering as you think
1) They don't make LP fridges that small, 12v won't push a fridge, and i'm pretty sure most run with the generator or inverter (i know mine in my older forest river did)
2) Coming from a long background in the AV industry, the HDMI Matrixing switch that would be needed to reliably distribute are really expensive and prone to fail. Even a basic HDMI switch is really prone to fail unless you're spending hundreds of dollars on one. And you either have to run long HDMIs (expensive and impossible to repair/replace in an RV) or use CAT5e to HDMI baluns to carry the HD signal (expensive and temperamental)
3) multiple inputs allows you to mix broadband modem,sat,etc from room to room, if they were all on a single switch you could only distribute one signal.