You'll hear endless repetitions of the concept that filament life is a function of temperature, a convenient explanation that is both true (you can change the life by changing the voltage, which affects temperature) and false (not all filaments at the same temperature have the same life). That is because temperature is not the
only independent variable in the life equation.
since we are keeping voltage constant.
What am I overlooking?
Most of the design space, if you think in terms of constant voltage. The higher the voltage, the longer and/or thinner the filament must be to get the same power dissipation. This reduces luminous efficacy and life, since the power is spread over a larger area (in a relation of length and cross-section to surface area, length dominates) (longer and thinner means more fragile). Automotive bulbs have much longer lives compared to house bulbs, and 120V bulbs much longer lives than 240V bulbs. And higher luminous efficacy!
There are more blind spots in this discussion, but the biggest one is the steady state assumption. If temperature corresponded with life, we would expect that bulbs of the same design would cluster around the same life time in terms of "on hours". But what actually happens is that a significant number last for 0 hours! If you've ever had a motion-activated "security" light, you know that they burn out bulbs at a ferocious rate. It's almost as if life should be counted in switching cycles rather than on hours...
What mechanism can explain the frequent (nearly universal) observation that burnout coincides with switching? The filament has a
temperature coefficient. When turned off, it is at room temperature (or colder for exterior lamps; generally, ambient temperature). The temperature coefficient of resistance is positive, so as temperature increases, so does resistance. That makes cold resistance much lower than operating resistance. Say that a 240V lamp has a power dissipation of 60W. That means that its operating resistance should be around 1K ohms. Suppose it operates at 3000 °C. Then its cold resistance (from the tungsten tempco of 0.0045) is just 75 ohms. So during the first few milliseconds after it switches on, its power consumption is over 750 watts! And the wiring etc has no difficulty delivering that much current.
When such a large amount of power is focused in a small object, heating is also rapid. Unfortunately, the filament does not have uniform cross-section at the atomic level, so there will be some regions where heating happens first. Metal will boil away faster in these areas, thinning them down further, and the local heating becomes progressively more intense. These are the places where the filament will eventually, on one of these switch-on events, break and end its useful life.
There are also ways to mitigate this process, and they have been known for a very long time. This is really basic stuff, nothing fancy that you could patent or build a company on. It was probably known by Edison a hundred years ago.