The boats that I have owned over the past 14 years had the power (Yellow) wire directly connected to the battery as part of the OEM wiring. I kept the batteries in the boat year-around, charging them every couple of months during the off-season.
The stereo never ran down the batteries over the course of those years. I suppose, maybe if I left the boat/batteries un-charged for longer, like 4-6 months, then perhaps the stereo 'keep alive' would run down the batteries.
So, I would not consider it wrong to do the 'direct connect' thing with the yellow wire, and probably a lot of boats are already wired up that way. You just need to understand what the limits of that approach are.
My cars happen to be the same way . . . if I don't run them for 4-6 months, the battery seems to die . . . :noidea:
