I think it needs emphasising here that the SEN case isn't simply one whereby an airport is calling itself London, as certainly is the case with CBG and OXF etc.. The fact is that IATA have accepted that SEN is justifiably a London airport, whereas they are extremely unlikely to do so for the others mentioned.
Perhaps the LCY management are not aware that SEN is preferred alternate for BA Cityflyer, Cityjet and a few others. I would suggest that those carriers do not share the view of SEN being " ......a field on the East coast.", but the best choice in terms of minimising passenger inconvenience and schedule disruption.
Tagron
One of the main aims of IATA in designating which airports serve a particular city is that it enables travel agents worldwide to offer their clients a choice of flights to a number of suitable airports, which they could not do otherwise without local knowledge of the area. I agree with your perhaps tongue-in-cheek idea in principle but it would actually only produce more confusion for the traveller.