Exactly. Heathrow was setup as an airport in the middle of the last century, and continues to be used as if London hasn't grown in that time, and won't grow in the future. With plans to extend. I regularly get woken at 4:30am. Undoubtedly, at some point during the day I'll see headlines or commentary about mental health or strain on the NHS. I wonder how many would be feeling considerably better if they simply weren't subjected to sleep deprivation and a plane flying overhead every 120 seconds.
By that logic, London should build their airport about 2 hours by train away from the city, because anything within <2h radius is still within highly populated zones.
2 hours by HSR is a very long way ~300 miles from London. In reality, 50 miles north east of London is farm land.
The core problem is when you build an airport you decrease the value of all nearby property. If people building airports directly compensated people say 50,000$ each property they would build airports in the middle of nowhere and opposition would likely be minimal. Instead people suddenly hate where their living but can’t afford to move.
Not everything is connected by HSR. Getting from Heathrow to city centre can take ~1.5h on public transport, and that's like ~15 miles in straight line.
If you're building an airport you can presumably also build other infrastructure. I am not saying it needs to be reach it in 20 minutes via HSR, just that distance is not the problem infrastructure is.
Dulles airport was built 30 miles from DC in what was the middle of nowhere at the time even though DC already had an airport. "In 1965 Dulles averaged 89 airline operations a day while National Airport (now Reagan) averaged 600 despite not allowing jets." Dulles still does not have a subway link to DC, and it's not the closest airport yet it still sees 21 million passengers a year.
The problem is that access to the airport becomes a location amenity for some businesses, which in turn will draw housing for workers, and eventually the city will envelop the airport.