I thought that the unsurmountable issue with the Thames Estuary airport was the bird-migration routes that have existed for thousands of years ? It would be unlikely that the various bird species would alter their behaviour and would make safe flying impossible in the vicinity due to engine ingestion.
In theory it would have made eminent sense for London, compared to the ring of airports currently in operation from a noise and emission standpoint, especially with a hyperlink to whisk passengers to/from the location. Sadly such a utopian port will be unlikely. We have Prestwick, if our Scottish cousins haven't broken away by then. Except for a small number of the population, we are all guilty of using the transport options that cause us the most irritation.
why HS2 isn't going via Heathrow I don't understand and also connecting with HS1?
Indeed, the puzzling strategies of the UK transport authorities. Europe has mainline stations at nearly all the major airports in each country, in the UK I can only think of Gatwick, Luton (sort of) and Southampton off the top of my head, although branch lines go to some others. No joined up thinking.