Resistive heaters lile a lightbulb are much less efficient than a heat pump. You'd still be better off with the led.

No, because the light can escape through windows.

So can heat. That's not the appliance's fault.

It's not about fault at all - I'm just saying that the analysis does not apply to lightbulbs. For a lightbulb to be as efficient as a resistance furnace at heating a room, you would need to have zero light escape that room so that all the light would be converted to heat. Then, the heat would leave the room at the same rate as heat generated by a resistance furnace.

Even if we consider incandescent light bulbs, which waste most of the energy they use as "heat", that heat is actually being transferred primarily through radiation, so it can escape through windows more easily than the heat that a furnace transfers to your indoor air.

Thermal infrared doesn't go through glass. You only lose a negligible amount of visible light. It's still 100% efficient as an integer percent.

I assume by “thermal infrared” you mean the IR produced by approximately room temperature objects. Incandescent bulbs produce much higher energy infrared because the filament reaches about 2000 Celsius. Those higher energy waves can go through glass.

Right, that's true, I was thinking about it wrong.

Still, not much is going to hit a window on average. So maybe 90% efficient.

You do realize that burning natural gas for heat produces light as well right?

Natural gas furnaces are designed to not let that light out. Instead, the light is absorbed by the surfaces of the furnace and turns into heat. The inefficiency in gas furnaces is heat leaving in the exhaust.

The heat isn't where you want it.