Poor-Man's Power Meter
A significant difference to a hot-wire ammeter is that the resistance of the bulb varies with the temperature, whereas the material of an ammeter is chosen to have a very low temperature coefficient of resistance.
To first order, this won't matter, as you are driving the lamp to the same temperature in the calibration phase. However, not knowing the resistance, and having it vary from run to run, could cause you difficulties in driving the lamp consistently.
Detectors of this type have been used for RF measurements, where the working temperature of the lamp is chosen to make its resistance 50 Ω. DC is applied to heat the lamp, and the resistance is servoed to 50 Ω rather than controlling the light output or temperature. When RF is applied, the increased power causes a drop in the DC required to maintain the same temperature.
For very unusual waveforms, say with crest factors exceeding 5:1, this might be better than using commercial RMS to DC converters.