I agree it's not constant power (that would be a hell of coincidence) but I think there is a bit more to it, not least because the starting battery is not a fixed or unlimited voltage or current source.
For example, if the load on the starter is higher due to cold temperatures, the starter speed will be slower, but the current will be greater and the voltage will be lower. Well, until the point I=V/R kicks in as the battery voltage has sagged.