If I am heating the house anyway, does an inefficient light bulb actually waste anything?

The argument is sound as far as it goes and it fails on one crucial point: it assumes your heating converts electricity to heat at the same rate the bulb does.

If you heat with a resistive electric heater, that is true. A joule of electricity gives a joule of heat either way, and in that specific case an inefficient bulb genuinely costs nothing extra during the heating season.

But if you heat with a heat pump, it is not true at all. A heat pump does not convert electricity into heat — it uses electricity to move heat from outside to inside, and it delivers several units of heat per unit of electricity consumed. Three or four is typical, more in mild conditions.

So the bulb's waste heat costs you one unit of electricity for one unit of heat, while the heat pump would have delivered that same unit of heat for a quarter of the electricity. The inefficiency is real and the ratio is large.

There is a second failure that is independent of the economics: heat in the wrong place.

Heating systems put heat low in a room, usually deliberately, because warm air rises and you want the occupied zone warm. Lights are at the ceiling. Heat delivered at ceiling level largely stays there, which is why high rooms are famously hard to heat.

So even in the perfect resistive-heating case, a unit of heat from a ceiling fitting is worth less to your comfort than a unit from a radiator. Not worthless, but the substitution is not one for one.

Also worth noting for completeness: the summer case reverses everything. If you ever run air conditioning, the waste heat costs you twice — once to produce it and again to remove it.

The same argument applies if you heat with anything cheaper per unit of heat than electricity — gas, oil, wood, district heating.

In most places electricity costs several times more per unit of energy than gas. So replacing gas heat with bulb heat is an expensive way to warm a room even at perfect efficiency, before you consider that the bulb was supposed to be producing light.

Which gives the general rule: the argument only works when the marginal cost of heat from your heating system equals the marginal cost of heat from the appliance. That is true for resistive electric heating and essentially nothing else.

Two practical points that usually decide it regardless of the physics.

Lifetime. Efficient bulbs last far longer than incandescent ones. Even in a scenario where the energy is free, you are replacing the old type many times more often, and in an awkward fitting that is the real cost.

The bulbs are already gone. In most markets the inefficient options have been withdrawn, so the choice you are analysing is largely hypothetical outside a few special-purpose fittings.

The thought experiment is still worth doing, because the reasoning transfers directly to appliances that genuinely do produce a lot of waste heat and that you do still choose between.