I don't know much about the electronics.As bernard has said, it's down to the powering of the 'electronics' which produce the run-on delay. If the supply for the electronics was derived from the S/L., rather than the permanent L, the fan would probably come on when the light was switched on, but the fan would then go off immediately the light was switched off, because the electronics sustaining the run-on would also have lost its supply.
To get around that would not be impossible, but would introduce more complexity, since a way would have to be devised to maintaining 'alternative' supply to the electronics after the light had been switched off - either with a battery (or very large capacitor) or by 'switching' to a supply derived from the perm L during that period.
Maybe I haven't thought this through well enough, but what I don't really understand is why they do not (as with cheap LED 'lamps') use a capacitive 'dropper', rather than a resistor, in which case the heat (and most of the 'energy wastage') would go away.
However, it is my belief that a timer fan is always switched on by the timer connection (even when set to no time delay). That is why the Switched live has to be connected to both PL and SL(LT) when only L and N are available. The fan then stops when the supply is removed from both - because there is no supply..
So, with three wires: PL, SL & N, could not a timer be triggered by the SL being switched on which then connected the PL to whatever needed it until the timer switches off - when it would be disconnected until the next time?
Could that not be achieved by the electronic equivalent of a timer and a relay?
Well, yes, I know it could but why isn't it? How much can it cost?
Apart from being very cheap, if that is the reason, why would something be designed to be drawing current continuously if used possibly only once or twice a day?