An inter-airport rail link would serve – who exactly?
Passengers flying into one airport and out of the other.
How much would these passengers be willing to pay for this facility?
The same as they pay currently for walking for five minutes from gate to gate at Paris, Frankfurt or Amsterdam - nothing.
Consider, for example, a passenger from Turin to Toronto. Right now, he has a choice of hubbing through AMS, PAR, FRA, ZRH, ROM, probably MAD, LIS and CPH as well.
Or flying BA into LGW and schlepping across to LHR (at his own expense) around the M25.
BA would love to have the capacity available at LHR to bring Turin – and other secondary European destinations – back to the main hub. It would be a huge multiplier to their network. But the passengers they would grab back from Air France, Lufthansa etc will only be persuaded by a simple transfer within a single terminal, certainly not a rail (or helicopter) journey between two airports.