Also if the current of a heater goes up, the heat output increases so the thermostat will turn it off sooner. As long as the power doesn't rise to a level that the heater can't tolerate, the consumer is not paying any more. Higher wattage for less time = the same kWh and BTUs.
I agree in the case of a regulated heater, but in the case of incandescent bulbs and capacitive droppers it would be detrimental. Incandescent bulbs not only draw more current they fail faster too. It's probably a safe bet that if you increase the voltage the the current will increase, by how much is hard to guess.
I doubt incandescent lamps are a large proportion of the load nowadays and will rapidly be replaced with alternatives or by ones rated to the new mains supply voltage, if that's not practical.
Decent quality LED lamps use a proper switched mode power supply, so increasing the voltage will reduce the current.
There's a device available in the UK, which is supposed to save energy, by regulating the mains voltage at 220V, using a buck transformer. In reality it makes little or no difference, for the reasons mentioned above.