I suppose that these are safe, but I worry anyway.
From my youth, I was taught that all fire needs a source of fuel (gas, wood, propane, etc.) and a place of exhaust. A gas stove uses so little gas, and is so pure, that the amount of waste product is minimal and dissipates in the air of the kitchen.
A gas fireplace has considerably more burners than a stove. My worry is that the combustion is not 100% (although close, like a stove), and there is enough residual unburnt gas that it could cause issues in the house.
But like I said, maybe I am worrying too much.