All true, and if one reduces the resistance of the dropper appropriately for that reduced RMS voltage, the power supplied to the heaters will, indeed be the same 'as normal', and I now agree that will result in an appreciable reduction in the dissipation (hence heat production) in the dropper.If you put a diode in series with the load the RMS voltage becomes 1/root2 of the original. With a 240v supply that becomes approx 170V. Then you design the dropper as if you are using a 170V supply.
However, as I've been saying, an issue arises because of the peak current the heater filament will be subjected to in this situation - since the peak voltage (hence peak current, for a resistive load), is sqrt(2) times RMS for 'full AC", but 2 times RMS for half-wave rectified AC.
If one takes, for example a valve with a heater rated at 6.3V (RMS) 0.3A for 'full AC' (or 6.3V 0.3A DC) (i.e. about 1.9W) then if one feeds that with half-waved rectified AC of the same RMS voltage (6.3V) (so as to achieve the same heater power of 1.9W), the peak voltage will be 12.6V, rather than 8.9V, and the peak current 0.6A, rather than 0.42A - which one might expect to potentially have a marked effect on survival of the filament ....
... it's roughly equivalent to taking an incandescent bulb/lamp, designed as 60W at 240V (RMS, full AC), hence 0.25A RMS, and instead trying to run it at the same power by supplying it with every positive (or every negative) half cycle of a 340V RMS supply, the peak current then being around 0.5A, rather than 0.35A with the 'normal' supply.
Kind Regards, John