If it comes up from the floor/slab inside of the drywall there should be zero chance of freezing even if it is capped. There would have to be some truly serve cold for an occupied and conditioned house to freeze pipes there.
If the water is 180*F there isn't much I would want to use it for. Anything that temperature you come in contact with it going to be unpleasant. I suppose if you were able to limit the flow rate you might be able to keep an object at a safe temperature.
If it were my project I would consider building out the wall, or a half wall with a ledge on top, and running the line somewhere else -it could easily be run in the inside walls once it reached- and placing a heater somewhere else in the bathroom. The bathroom is one room I would like warm, removing the heater sounds like a recipe for a cold bathroom.