Reminds me of BHX where they charge £1 for cars dropping off passengers to the airport - the only way to avoid the charge is to get dropped off at the NEC and take the shuttle train.

I can see it working by charging all private cars entering the central area via the tunnel for T123, not sure about T4 and T5. Also, as many have stated, the public transport at LHR is focused on Central London - if your coming from other directions (further than a bus ride) then car is the most realistic choice.