That makes sense for the stereo. But the constant 12 volts the adaptor for the tv outputs is what the tv is designed for. The "12 volts" on a boat is anywhere from 12 to 14.4 volts in reality. Some tvs don't mind, some are very voltage sensitive. A dc to dc adaptor would be a good idea. It would keep it within the tv specs and there would be no possible issues.
Living aboard in Victoria Harbour