edit: misread the comment at first but edited since the core argument still stands.
No, US airports work that way because of bizarre bureaucratic funding rules. Sensible airports like Frankfurt or Amsterdam (or even Heathrow) connect directly to the city's ordinary transit network.
1. underground to London Paddington
2. Heathrow Express to London Paddington
3. bus to Reading to get on intercity train to Bath
4. bus/coach from Terminal 3/4 station to Bath
The train to Bristol & Cardiff passes Heathrow just a few miles away, but there is no direct rail connection at all.
It's almost as bad as here in New Mexico, where our only state-level railway, connecting Santa Fe and Belen via Albuquerque, fails to go to the Albuquerque airport, which is the destination/origin for so many Santa Fe travellers.
The train is there, you could also get Crossrail (old Heathrow Connect) to Hayes & Harlington (or Ealing Broadway). Heathrow Express into Paddington and then out again ends up being faster because the fastest trains are the limited-stop expresses, but that's a question of rail network optimization and happens in all sorts of places (e.g. back when I lived in North London the train to Cambridge went through the rail station nearest my house (Harringay), but it was quicker for me to go into King's Cross and out again). Physical distance has very little to do with it. Most people arriving at Heathrow are not going to Bath (a city of less than 100K, compared to London's 9M) and most people going to Bath are not coming from Heathrow; having to change at a hub isn't that unreasonable.
However, the rail system exists. Every train stops at Reading. The trains also go to the capital and largest city in Wales (Cardiff) and Bristol (the 10th largest district by population in the UK). Access to this intercity rail line requires back-tracking into London, something that I don't consider absurd, but do consider a bit silly.
Also, taking population considerations and making them central can lead to strange results in the UK. 1/6th of the population lives in the London metro. While that's important from some perspectives, it can't be the overriding principle for integrated transportation.
Which is not wrong, but also doesn't quite capture all the complexities of flying, especially inter-continentally.
It's not quite as simple as has an airport or not - Nuremburg and Stuttgart do have airports - but major intercontinental airport or not. Airports are and should be set up with their "catchment area" in mind (bearing in mind what neighbouring airports exist), and their transport connections set up to support that.
Frankfurt is the main intercontinental airport for a region with several mid-sized cities, and its transport links are set up to support that. The London airport system is already the busiest in the world, so transport links are - rightly - focused on spreading people through London rather than long-distance services to other places. (E.g. elsewhere in the thread you mentioned Bath - but Canary Wharf, one of the places Heathrow was recently connected to by Crossrail, employs more people than the entire population of Bath).
so...it'll be worse